What is the integral of sin(x)*2x ?

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

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integral of sin(x)*2x

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

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

Solution steps

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

Take the constant out:

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

= 2 \cdot \int sin (x) 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

\frac{\partial}{\partial x} (2 e^{y} x)

\int \frac{6 x ^{3} + 3 x ^{2} - 46 x - 21}{x ^{2} - 9} d x

\frac{\partial}{\partial y} (2 x)

\int \frac{( 1 + x ) ^{2}}{x} d x

\int 1 + 4 x - x^{2} d x

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