What is the integral of 3θcos(θ) ?

The integral of 3θcos(θ) is 3(θsin(θ)+cos(θ))+C

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integral of 3θcos(θ)

\int 3 θ cos (θ) d θ

3 (θ sin (θ) + cos (θ)) + C

Solution steps

\int 3 θ cos (θ) d θ

Take the constant out:

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

= 3 \cdot \int θ cos (θ) d θ

Apply Integration By Parts

: θ sin (θ) - \int sin (θ) d θ

= 3 (θ sin (θ) - \int sin (θ) d θ)

\int sin (θ) d θ = - cos (θ)

= 3 (θ sin (θ) - (- cos (θ)))

Simplify

= 3 (θ sin (θ) + cos (θ))

Add a constant to the solution

= 3 (θ sin (θ) + cos (θ)) + C

\frac{d}{d x} (\frac{x ^{2} - 8}{x - 3})

2 y^{^{''}} - 4 y^{^{'}} + 4 y = e^{x} sec (x)

\int csc^{2} (d) x d x

\int \frac{2 y - 1}{x ^{2} + 1} d y

What is the integral of 3θcos(θ) ?
The integral of 3θcos(θ) is 3(θsin(θ)+cos(θ))+C