Question

How do you integrate sinx/ cost?

Answer 1

can you rewrite the ques?

Answer 2

Integral sinx divided by cosx ex

Answer 3

Dx

Answer 4

\[\int\limits \frac{ \sin x }{ \cos x e ^{x} } dx\]

Answer 5

can you make a substitution here?

Answer 6

Just take off the ex that was a typo

Answer 7

okay in that case just make a substitution
let u = cos x

Answer 8

you know substitution rule right?

Answer 9

Ok

Answer 10

Yes

Answer 11

I need step by step
Please

Answer 12

since you're making a u substitution, that means you need to integrate in terms of u and not x

basically you need to find dx in terms of du

since you have u = cos x

we take the derivative

du= - sin x dx

dx= -du/ sin x

substitute that back into your integral

then integrate

once you've integrated, substitute u back into the equation

Answer 13

Oh ok.so how does it look like when I substitute it back. Because I did and it doesn't look right

Answer 14

\[\int\limits_{}^{} \frac{\sin x}{\cos x} dx \]
\[u=\cos x\]
\[\int\limits_{}^{} \frac{\sin x}{u} dx \]
\[du = (- \sin x) dx\]
\[-du = \sin x dx\]
note that we have sin x dx on the top of hte original integral and that it is equal to - du
\[\int\limits_{}^{} \frac{-1}{u} du \]

now integrate

the substitute u back in

Answer 15

Thank you so much!