What is the integral of (cos^2(x))/(1+sin(x)) ?

The integral of (cos^2(x))/(1+sin(x)) is cos(x)+x+C

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integral of (cos^2(x))/(1+sin(x))

\int \frac{cos ^{2} ( x )}{1 + sin ( x )} d x

cos (x) + x + C

Solution steps

\int \frac{cos ^{2} ( x )}{1 + sin ( x )} d x

Rewrite using trig identities

= \int - sin (x) + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int sin (x) d x + \int 1 d x

\int sin (x) d x = - cos (x)

\int 1 d x = x

= - (- cos (x)) + x

Simplify

= cos (x) + x

Add a constant to the solution

= cos (x) + x + C

f (x) = ln (x + 3)

\frac{\partial}{\partial x} (x^{2} (1 + y)^{3})

\frac{d}{d y} (\frac{e ^{y} + e ^{- y}}{2})

\frac{d}{d x} (\frac{1}{3} sin^{3} (x) - sin (x) + 1)

x \to 4 lim (\frac{x + 4}{x + 7})

What is the integral of (cos^2(x))/(1+sin(x)) ?
The integral of (cos^2(x))/(1+sin(x)) is cos(x)+x+C