What is the integral of xsin(2) ?

The integral of xsin(2) is 1/2 sin(2)x^2+C

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integral of xsin(2)

\int x sin (2) d x

\frac{1}{2} sin (2) x^{2} + C

Solution steps

\int x sin (2) d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= sin (2) \frac{x ^{2}}{2}

Simplify

sin (2) \frac{x ^{2}}{2} : \frac{1}{2} sin (2) x^{2}

= \frac{1}{2} sin (2) x^{2}

Add a constant to the solution

= \frac{1}{2} sin (2) x^{2} + C

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