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 (\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.