What is the integral of 7θcos(θ) ?

The integral of 7θcos(θ) is 7(θsin(θ)+cos(θ))+C

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integral of 7θcos(θ)

\int 7 θ cos (θ) d θ

7 (θ sin (θ) + cos (θ)) + C

Solution steps

\int 7 θ cos (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int θ cos (θ) d θ

Apply Integration By Parts

: θ sin (θ) - \int sin (θ) d θ

= 7 (θ sin (θ) - \int sin (θ) d θ)

\int sin (θ) d θ = - cos (θ)

= 7 (θ sin (θ) - (- cos (θ)))

Simplify

= 7 (θ sin (θ) + cos (θ))

Add a constant to the solution

= 7 (θ sin (θ) + cos (θ)) + C

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What is the integral of 7θcos(θ) ?
The integral of 7θcos(θ) is 7(θsin(θ)+cos(θ))+C