What is the integral of 2θcos(θ) ?

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

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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

: θ sin (θ) - \int sin (θ) d θ

= 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 0 lim (\frac{2 ^{2 x} - 2 ^{- 2 x}}{2 ^{3 x} - 2 ^{- 3 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 ∣})

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