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

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

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integral of (cos(θ))/(1+sin^2(θ))

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

arctan (sin (θ)) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{1 + u ^{2}} d u

= \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

\int \frac{1}{1 + u ^{2}} d u = arctan (u)

= arctan (u)

Substitute back

u = sin (θ)

= arctan (sin (θ))

Add a constant to the solution

= arctan (sin (θ)) + C

\int (1 + y e^{x y}) d x

\int \frac{1}{x ( ln ( x ) ) ^{2}} d x

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 1})

\int 18 x d x

\frac{d y}{d x}, 8 x^{3} + x^{2} y - x y^{3} = 9

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