Mastering Integration: Step-by-Step Methods Explained | Homework Help

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Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution

 

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clurt said:

Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution


Seems to me Exponential Expansion'd be better.. But what kind of question is this, anyways?
 
clurt said:

Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution

What have you tried?

Where are you stuck?

You must show an attempt before we can help you. -- See the rules.
 
im stuck everywhere and i have tried, can't produce anything
 
clurt said:

Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution


I don't think the questions are in parts, as such. I think you're supposed to choose the best option between those "parts" - i.e. if you think you can the integral directly, then choose the first option. If you think you should sub, choose the second, etc.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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