Self Improvement Tips & Resources

1) ∫(3x^2+4x^2-7)dx.
2)∫ (2x-1)(x^2-x^6)dx.
3)∫ x-1/4x^2-8x+10dx
4)∫(x+1)^2/x dx.
5)∫ 3e^2n dx,
6)∫ from 1to2 x^2e^x^3dx.

please help me solve I am studying Mathematics "self study"

1: simple polynomial calculus.

first, simplify integrand:
∫(7x^2 - 7)dx

Next, use the addition rule, constant multiplication rule, and power rule to do the simplest integration you can do:

∫(7x^2 - 7)dx = 7/3 * x^3 - 7*x + C

remember the C when doing indefinite integrals, you will loose points should you not.
————————————-
2: ∫ (2*x-1)*(x^2-x^6)dx.

Expand integrand and sort by power:
∫(-2*x^7 + x^6 + 2*x^3 - x^2) dx

Carry out integration as you normally would:
∫(-2*x^7 + x^6 + 2*x^3 - x^2) dx =

-1/4*x^8 + 1/7*x^7 + 1/2*x^4 - 1/3*x^3 + C
————————————–…
3) ∫(x-1/4 * x^2 - 8*x+10)dx

Still simple polynomial calculus. First sort by power and combine terms which can be combined:
∫(-1/4 * x^2 - 7*x + 10)dx =

-1/12*x^3 - 7/2*x^2 + 10*x + C
————————————–…
4: ∫(x+1)^2/x dx

Expand integrand, and then do the simple polynomial calculus. The 1/x is a little tricky, but recall that 1/x is the same as x^(-1). When you apply the power rule, it gets interesting because your term will have a 1/0 coefficient, which is against the rules. By a coincidence in mathematics, ∫(1/x)dx = ln(x) + C

∫(x + 2 + 1/x) dx =

1/2*x^2 + 2*x + ln(x) + C
————————————–
5: ∫ 3*e^(2*n) dx, if I understand you correctly. You might want to re-learn to use parenthesis and order of operations.

This is a trick question. n is a variable, but isn’t the variable of integration. Unless you tell me how n is a function of x, but since you didn’t, I must assume n is a constant.

Therefore the answer is
3*x*e^(2*n) + C
————————————-
6. int(x^2 * e^(x^3), x= 1..2), if I understand you correctly

Use the trick of u-substitution to solve ∫(x^2 * e^(x^3)) dx.

Define u = x^3 and take its derivative du = 3*x^2 dx

Can we spot the derivative in the original integral? yes, if we multiply by 1 in a fancy way (ahem, 3/3).

∫(x^2 * e^(x^3)) dx = ∫(3/3 * x^2 * e^(x^3)) dx

since du = 3*x^2 dx, replace this term with du. Replace our definition of u in the exponent. Factor the 1/3 out of the integration.

1/3 * ∫e^u du

∫e^u du is easy, it’s just equal to e^u + C. The natural exponential has this nice property.

Therefore, including the definition of u and the 1/3 factor, the final result of the indefinite integral is
1/3 * e^(x^3) + C

Plug in the limits:
int(x^2 * e^(x^3), x= 1..2) = [1/3 * e^((2)^3)] - [1/3 * e^((1)^3)]

Result:
1/3 * e^8 - e/3

Adopting a healthy lifestyle does not mean that we have to stop enjoying life.It does, however, mean taking responsibility for our actions.

1. get enough sleep
2. get proper nutrition
3. get sufficient exercise
4. have access to clean drinking water
5. practise proper sanitation methods
6. get vaccinated

Before people answer, I truly am very aware that the best approach is to simply reduce anxiety and stress. Sometimes though it’s nice to have a little helping hand, as stress hormones like cortisol can be harmful to the body. I was just wondering what natural remedies are best at balancing cortisol

I heard Rhodiola Rosea, Ashwaganha and Reishi Mushroom are good but I don’t really know, and would love some opinions!

Thanks guys
The natural and most effective way is to take DHEA, this is a hormonal precursor made by the adrenal glands, but over time less and less is produced. It is the direct antagonist in the body to cortisol. DHEA can be purchased otc in any supplement store, start with 25mg daily and work up gradually to to 100mg a day.

What kind of thoughts are you wanting to change? If you mean pessimistic thoughts, try Authentic Happiness by Martin E. P. Seligman.

Hello, I want to start my own little holistic/energy healing business in a few years. Once I get a certificate in holistic healing then where do I go on from there? The shop will have an energy healing room, and then a big room with merchandise,art,etc.

Word of mouth testimonials sounds ideal for that kind of venture.

I know that holistic-self descriptions are things like "I am me" and "I am a human being." But what do they say about yourself if you choose to use more holistic self-descriptions?

I’m asking because I did an experiment in psych class where I ended up describing myself with an equal number of social self-descriptions "I am a sister, I am a student, etc" and Holistic self-descriptions "I am me."

I didn’t use any physical self-descriptions and I used a few psychological self-descriptions.

Do holistic self descriptions say you lack a personal identity or does it say the opposite, that I am secure in my personal identity? I’m curious because according to the sheet our professor handed to us holistic descriptions are defined as "so comprehensive or vague that they do not distinguish one person from another."

It would help if the answer-er studied psychology, so I know you’re not just going by gut feelings or psychobabble with your answer.
I wanted to add that the thing that’s throwing me off is our hand-out’s description of "holistic." It says "comprehensive or vague." Comprehensive is a totally different adjective than vague. Comprehensive means complete, all-inclusive, far- reaching. Vague means abstract and unclear. At least it said comprehensive OR vague instead of comprehensive AND vague but it’s still not a clear definition.

Virtually anytime the term ‘holistic’ is thrown around, it is utter garbage. Your personal identity is just that, personal. We are social creatures, so of course there are going to be some homogenization. If everyone was absolutely different, then society would never have developed. We are very similar in most ways, but that doesn’t mean we aren’t different.

Trying to describe yourself with words is not nearly as functional as defining yourself with actions.

The oven does not seem to be cleaning itself. I’ve heard that there could be something wrong with the clock that would make this happen, so any info about resetting the (old, analog) clock on this oven would be helpful too.
I finally got the oven door open by setting the oven to actually clean - it hadn’t been before. After the 3 hour cleaning cycle, the oven door opened. Unbelievable. Thanks for the ideas everyone.

u need to flip ur breaker that controls the kitchen and leave it off for at least a minute so the oven has a chance to reset it self

For a stupid snowed in bet the other night, among other things was to use the 3 bottles of deep dark self tanner that was at the house. Needless to say I look ridiculous! How long will this stuff last? It’s been 3 days and no change
Some self tanners can last up to 7 days… especially if you put a lot on.
Here are some tips on how to remove it!!
First you need to take a shower exfoliate your skin REALLY good!!
After you do that rub of a lemon wedge on your skin. Simply massage the wedge quickly over the area in question. This will usually lift the tanning lotion’s unwanted color. Lemon is the key here!!

OR a small amount of rubbing alcohol on a washcloth will work for small areas of error or excess as well. Give your skin a break between attempts.

There are two products that I know of that also remove self tanner one is the St. Tropez Self Tan remover or the Model Co. Tan remover.

I am doing a project on Holistic Healing in Spain and in any country in South America that speaks spanish also. Any website with information on the following in these locations would be appreciated: Reiki Healing, Angel Therapy, Crystal Healing, Where healing originated first in Spain, Famous Holistic Healers in Spain/South America, Meditation, Courses and Workshops on Healing in Spain, and anything basically to do with alternative and holistic healing!!Thanking you.

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You should seek help if you are self harming, because you it does tend to get worse as time goes by, and the quicker you seek help the easier it is to stop.
Just think, if you can stop it now, you will reduce the amount of horrible scars you make.
It doesn’t necessarily mean you’re ill, just going through some bad times and that’s the way you cope.