What is the integral of 2xsin(x) ?

The integral of 2xsin(x) is 2(-xcos(x)+sin(x))+C

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integral of 2xsin(x)

\int 2 x sin (x) d x

2 (- x cos (x) + sin (x)) + C

Solution steps

\int 2 x sin (x) d x

Take the constant out:

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

= 2 \cdot \int x sin (x) d x

Apply Integration By Parts

: - x cos (x) - \int - cos (x) d x

= 2 (- x cos (x) - \int - cos (x) d x)

\int - cos (x) d x = - sin (x)

= 2 (- x cos (x) - (- sin (x)))

Simplify

= 2 (- x cos (x) + sin (x))

Add a constant to the solution

= 2 (- x cos (x) + sin (x)) + C

y^{^{'}} + 8 y = t + e^{- 7 t}

5 x^{3} - 6 cos (x)

f (x) = \frac{2}{x - 8}, (10, 1)

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

\int \frac{8}{x ^{2}} d x

What is the integral of 2xsin(x) ?
The integral of 2xsin(x) is 2(-xcos(x)+sin(x))+C