# Thread: Integration with substition

1. ## Integration with substition

Integrate

They gave me the U for this integral but im not sure how im suppose to work it into the problem. Can someone show me the steps to do this?

2. Originally Posted by NickytheNine
Integrate

They gave me the U for this integral but im not sure how im suppose to work it into the problem. Can someone show me the steps to do this?
it's a substitution problem, and they gave you the substitution, just follow the method. what are you supposed to do next? find du ...

3. Originally Posted by NickytheNine
Integrate

They gave me the U for this integral but im not sure how im suppose to work it into the problem. Can someone show me the steps to do this?
$\displaystyle \int\frac{\sec^2\left(\frac{1}{x^{39}}\right)}{x^{ 40}}dx$

If we let $\displaystyle z=\frac{1}{x^{39}}$ then $\displaystyle dz=\frac{-1}{x^{40}}$. So

$\displaystyle \int\frac{\sec^2\left(\frac{1}{x^{39}}\right)}{x^{ 40}}dx\overbrace{\mapsto}^{z=\frac{1}{x^{39}}}-\int\sec^2(z)dz$

4. so the final answer would be -tan(1/(x^39)) + C
is this correct?

5. Yes.