Question

help a brother out with calculus or ya renk thank you

Answer 1

As given by the question

There are given that the integral:

$\int \frac{\cos^3(x)}{1-\sin^2(x)}dx$

Now,

Apply the formula in the denominator

Then,

From the formula

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

So,

$\int \frac{\cos^3(x)}{1-\sin^2(x)}dx=\int \frac{\cos ^3(x)}{\cos ^2x}dx$

Then,

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

Hence, the correct option is B.