What is the integral of (θ^2-csc^2(θ)) ?

The integral of (θ^2-csc^2(θ)) is (θ^3)/3+cot(θ)+C

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integral of (θ^2-csc^2(θ))

\int (θ^{2} - csc^{2} (θ)) d θ

\frac{θ ^{3}}{3} + cot (θ) + C

Solution steps

\int θ^{2} - csc^{2} (θ) d θ

Apply the Sum Rule:

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

= \int θ^{2} d θ - \int csc^{2} (θ) d θ

\int θ^{2} d θ = \frac{θ ^{3}}{3}

\int csc^{2} (θ) d θ = - cot (θ)

= \frac{θ ^{3}}{3} - (- cot (θ))

Simplify

= \frac{θ ^{3}}{3} + cot (θ)

Add a constant to the solution

= \frac{θ ^{3}}{3} + cot (θ) + C

y = x^{2}, y = 7 + x

\int e^{4 x} sin (4 x) d x

\frac{1}{( 1 - s ) \cdot ( s ^{2} + 1 )}

y^{^{'}} (x) = \frac{9 x ^{2}}{9 y ^{2} - 7}, y (1) = 0

\int \frac{x + x ^{2}}{x ^{3}} d x

What is the integral of (θ^2-csc^2(θ)) ?
The integral of (θ^2-csc^2(θ)) is (θ^3)/3+cot(θ)+C