What is the integral of 6θcos(θ) ?

The integral of 6θcos(θ) is 6(θsin(θ)+cos(θ))+C

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integral of 6θcos(θ)

\int 6 θ cos (θ) d θ

6 (θ sin (θ) + cos (θ)) + C

Solution steps

\int 6 θ cos (θ) d θ

Take the constant out:

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

= 6 \cdot \int θ cos (θ) d θ

Apply Integration By Parts

: θ sin (θ) - \int sin (θ) d θ

= 6 (θ sin (θ) - \int sin (θ) d θ)

\int sin (θ) d θ = - cos (θ)

= 6 (θ sin (θ) - (- cos (θ)))

Simplify

= 6 (θ sin (θ) + cos (θ))

Add a constant to the solution

= 6 (θ sin (θ) + cos (θ)) + C

\frac{x + 2}{4 x - 3}

\int \frac{x}{( x ^{2} - 2 x + 5 )} d x

y^{^{'}} = y^{2} - 3 y

\int x (2 x + 5)^{8} d x

\int e^{x} 4 - e^{2 x} d x

What is the integral of 6θcos(θ) ?
The integral of 6θcos(θ) is 6(θsin(θ)+cos(θ))+C