What is the integral of θcos(θ) ?

The integral of θcos(θ) is θsin(θ)+cos(θ)+C

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integral of θcos(θ)

\int θ cos (θ) d θ

θ sin (θ) + cos (θ) + C

Solution steps

\int θ cos (θ) d θ

Apply Integration By Parts

: θ sin (θ) - \int sin (θ) d θ

= θ sin (θ) - \int sin (θ) d θ

\int sin (θ) d θ = - cos (θ)

= θ sin (θ) - (- cos (θ))

Simplify

= θ sin (θ) + cos (θ)

Add a constant to the solution

= θ sin (θ) + cos (θ) + C

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