What is the integral of sin(k)x ?

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

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integral of sin(k)x

\int sin (k) x d x

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

Solution steps

\int sin (k) x d x

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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