What is the integral of θ^3cos(θ) ?

The integral of θ^3cos(θ) is θ^3sin(θ)-3(-θ^2cos(θ)+2(θsin(θ)+cos(θ)))+C

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integral of θ^3cos(θ)

\int θ^{3} cos (θ) d θ

θ^{3} sin (θ) - 3 (- θ^{2} cos (θ) + 2 (θ sin (θ) + cos (θ))) + C

Solution steps

\int θ^{3} cos (θ) d θ

Apply Integration By Parts

: θ^{3} sin (θ) - \int 3 θ^{2} sin (θ) d θ

= θ^{3} sin (θ) - \int 3 θ^{2} sin (θ) d θ

\int 3 θ^{2} sin (θ) d θ = 3 (- θ^{2} cos (θ) + 2 (θ sin (θ) + cos (θ)))

= θ^{3} sin (θ) - 3 (- θ^{2} cos (θ) + 2 (θ sin (θ) + cos (θ)))

Add a constant to the solution

= θ^{3} sin (θ) - 3 (- θ^{2} cos (θ) + 2 (θ sin (θ) + cos (θ))) + C

\int_{0}^{\frac{π}{3}} 2 + sin (3 x) d x

\int e^{- i w x} d x

(x - 1) y^{^{'}} + y (x - 2) = 0

f (x) = sin (2) x^{2}

x^{^{''}} - 5 x^{^{'}} + 6 x = e^{2 t}

What is the integral of θ^3cos(θ) ?
The integral of θ^3cos(θ) is θ^3sin(θ)-3(-θ^2cos(θ)+2(θsin(θ)+cos(θ)))+C