What is the integral of 1/(sin(θ)(cos^2(θ)+4)) ?

The integral of 1/(sin(θ)(cos^2(θ)+4)) is x/(sin(θ)(4+cos^2(θ)))+C

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integral of 1/(sin(θ)(cos^2(θ)+4))

\int \frac{1}{sin ( θ ) ( cos ^{2} ( θ ) + 4 )} d x

\frac{x}{sin ( θ ) ( 4 + cos ^{2} ( θ ) )} + C

Solution steps

\int \frac{1}{sin ( θ ) ( cos ^{2} ( θ ) + 4 )} d x

Integral of a constant:

\int a d x = a x

= \frac{1}{( 4 + cos ^{2} ( θ ) ) sin ( θ )} x

Simplify

\frac{1}{( 4 + cos ^{2} ( θ ) ) sin ( θ )} x : \frac{x}{sin ( θ ) ( 4 + cos ^{2} ( θ ) )}

= \frac{x}{sin ( θ ) ( 4 + cos ^{2} ( θ ) )}

Add a constant to the solution

= \frac{x}{sin ( θ ) ( 4 + cos ^{2} ( θ ) )} + C

What is the integral of 1/(sin(θ)(cos^2(θ)+4)) ?
The integral of 1/(sin(θ)(cos^2(θ)+4)) is x/(sin(θ)(4+cos^2(θ)))+C