1. ## integral

How do i start this problem
∫ 8 csc(8x-9)dx

2. $\int \csc{u} \, du = -\ln|\csc{u} + \cot{u}| + C$

3. i don't understand?

4. you don't know the antiderivative for the cosecant function?

5. no im sorry i sooooo lost. Can u show me step by step the test is 2morrow

6. skeeter continue plz this is helping me out as well

7. this one to

8. hey bigton we are in the same boat

9. this is an indfintie and definite integral evaluation problem

10. Originally Posted by theflyingcow
How do i start this problem
∫ 8 csc(8x-9)dx
the straight forward way to do this is by substitution.

let $u = 8x - 9$

$\Rightarrow du = 8~dx$

and low and behold, we have $8~dx$ in our integrand

thus, our integral becomes $\int \csc u~du$

11. so how do u continue it because i thought the 8 would be in front of the integral

12. Originally Posted by theflyingcow
so how do u continue it because i thought the 8 would be in front of the integral
$\int\csc(ax+b)dx\overbrace{\mapsto}^{u=ax+b}\frac{ 1}{a}\int\csc(u)du$

Let $v=2\arctan(v)$ to find the second integral

13. wow i never heard of arc

14. Originally Posted by theflyingcow
wow i never heard of arc
$\arctan(x)=\tan^{-1}(x)$

15. but my teacher never used inverse tan

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