# Basic Integration problem

• Krushnaraj Pandya
In summary, Mark44 is suggesting that substitution can be used to solve an integration exercise. Partial fractions are a standard method for solving integrals that are not found in tables of integrals.

Gold Member

## Homework Statement

∫(√x)^5/((√x)^7+x^6) dx

## Homework Equations

I have learned integration through substitution, trigonometric identities and standard integrals

## The Attempt at a Solution

I took (√x)^5 common which gave 1/(x+√x^7), Then I tried to substitute √x=t, √x^7=t but it just seems to complicate things more, I don't see any fruitful trigonometric substitutions either- would be grateful if someone can tell me how to proceed

Krushnaraj Pandya said:

## Homework Statement

∫(√x)^5/((√x)^7+x^6) dx

## Homework Equations

I have learned integration through substitution, trigonometric identities and standard integrals

## The Attempt at a Solution

I took (√x)^5 common which gave 1/(x+√x^7), Then I tried to substitute √x=t, √x^7=t but it just seems to complicate things more, I don't see any fruitful trigonometric substitutions either- would be grateful if someone can tell me how to proceed
Your substitution should work.
##t = x^{1/2} \Rightarrow t^2 = x \Rightarrow 2tdt = dx##
After you make the substitution, you should get an integral that you can evaluate using partial fractions.

Krushnaraj Pandya
Mark44 said:
Your substitution should work.
##t = x^{1/2} \Rightarrow t^2 = x \Rightarrow 2tdt = dx##
After you make the substitution, you should get an integral that you can evaluate using partial fractions.
The exercise in my textbook is supposed to be using the concepts I mentioned under relevant equations, therefore I need to solve it using that

Krushnaraj Pandya said:
The exercise in my textbook is supposed to be using the concepts I mentioned under relevant equations, therefore I need to solve it using that

Mark44 IS suggesting a method on your list---substitution. After that, partial fractions are a 100% standard method, and anybody who tells you you cannot use them is doing you a dis-service. Some integrals just cannot be done in any other way (except, maybe, by finding them in some "tables of integrals" somewhere).

Ray Vickson said:
Mark44 IS suggesting a method on your list---substitution. After that, partial fractions are a 100% standard method, and anybody who tells you you cannot use them is doing you a dis-service. Some integrals just cannot be done in any other way (except, maybe, by finding them in some "tables of integrals" somewhere).
ohh...ok, I'll use that then and see if I can solve it

Ray Vickson said:
Mark44 IS suggesting a method on your list---substitution. After that, partial fractions are a 100% standard method, and anybody who tells you you cannot use them is doing you a dis-service. Some integrals just cannot be done in any other way (except, maybe, by finding them in some "tables of integrals" somewhere).
I got the correct answer. Thanks a lot!