Find antiderivative of 6/7csc^2 x/7

Question

anonymous · Answer

the derivative of csc^2(x) is -cot(x) . hope this helps

anonymous · Answer

skipping steps:

= 6/7 * -cot(x/7) * 7
= - 6 cot(x/7)

let me know if you have questions

anonymous · Answer

+ constant ^_^

anonymous · Answer

I know that csc^2x equals -cot(x) but how did you solve it

jim_thompson5910 · Answer

Euler271 meant to say

the derivative of cot(x) is -csc^2(x)

or

the derivative of -cot(x) is csc^2(x)

jim_thompson5910 · Answer

the trick is to use u-sub 

let 

u = x/7

so

du/dx = 1/7

6du/dx = 6/7

6du = (6/7)dx

(6/7)dx = 6du

anonymous · Answer

but the 7's wouldn't cancel out

jim_thompson5910 · Answer

what do you mean

anonymous · Answer

the seven in (6/7) and the 1/7, does not cancel out the sevens.. giving me -6cot(x/7) + C
soo... how does the sevens cancel out in your answer?

jim_thompson5910 · Answer

I didn't cancel out the 7s though

jim_thompson5910 · Answer

do you see how I got du/dx = 1/7

anonymous · Answer

sorry but no, please explain in detail

jim_thompson5910 · Answer

ok I let u = x/7

because this is the argument of csc^2

jim_thompson5910 · Answer

then I derived both sides to get du/dx = 1/7

jim_thompson5910 · Answer

after that I multiplied both sides by 6 to get 6du/dx = 6/7

jim_thompson5910 · Answer

and then I multiplied both sides by dx to get 6du = (6/7)dx

jim_thompson5910 · Answer

So if we have this

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