What is the integral of θsin(θ) ?

The integral of θsin(θ) is -θcos(θ)+sin(θ)+C

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integral of θsin(θ)

\int θ sin (θ) d θ

- θ cos (θ) + sin (θ) + C

Solution steps

\int θ sin (θ) d θ

Apply Integration By Parts

: - θ cos (θ) - \int - cos (θ) d θ

= - θ cos (θ) - \int - cos (θ) d θ

\int - cos (θ) d θ = - sin (θ)

= - θ cos (θ) - (- sin (θ))

Simplify

= - θ cos (θ) + sin (θ)

Add a constant to the solution

= - θ cos (θ) + sin (θ) + C

\frac{d}{d x} (\frac{2 x ^{2} + 2 x + 2}{x})

ln (ln (3 x))

\frac{d}{d x} (\frac{x + 2}{x ^{2} + 2 x + 4})

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

x^{3} y^{^{'''}} - 6 y = 0