What is the integral of 2θcos(θ) ?

The integral of 2θcos(θ) is 2(θsin(θ)+cos(θ))+C

integral of 2θcos(θ)

\int 2 θ cos (θ) d θ

2 (θ sin (θ) + cos (θ)) + C

Solution steps

\int 2 θ cos (θ) d θ

Take the constant out:

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

= 2 \cdot \int θ cos (θ) d θ

Apply Integration By Parts

= 2 (θ sin (θ) - \int sin (θ) d θ)

\int sin (θ) d θ = - cos (θ)

= 2 (θ sin (θ) - (- cos (θ)))

Simplify

= 2 (θ sin (θ) + cos (θ))

Add a constant to the solution

= 2 (θ sin (θ) + cos (θ)) + C

x \to \infty lim (3 (1 + \frac{2}{x}) - x)

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

\int \frac{e ^{a r c t a n (x)} + 1}{1 + x ^{2}} d x

x \to - 1 - lim (\frac{x}{∣ x - 1 ∣})

\int 4 sin (x + \frac{π}{4}) cos (x - \frac{π}{4}) d x

What is the integral of 2θcos(θ) ?
The integral of 2θcos(θ) is 2(θsin(θ)+cos(θ))+C