Help a brother out with calculus or ya renk thank you

Question

asked Jan 13, 2023 40.5k views

1 Answer

Bill Grava · Answer 1 · 2023-01-19T19:29:09+0000

As given by the question

There are given that the integral:

$\int (\cos^3(x))/(1-\sin^2(x))dx$

Now,

Apply the formula in the denominator

Then,

From the formula

$1-\sin ^2x=\cos ^2x$

So,

$\int (\cos^3(x))/(1-\sin^2(x))dx=\int (\cos ^3(x))/(\cos ^2x)dx$

Then,

$\begin{gathered} \int (\cos^3(x))/(1-\sin^2(x))dx=\int (\cos^3(x))/(\cos^2x)dx \\ =\int \cos xdx \\ =\sin x+c \end{gathered}$

Hence, the correct option is B.