What is the integral of (sin(x)+sin(h)x) ?

The integral of (sin(x)+sin(h)x) is -cos(x)+1/2 x^2sin(h)+C

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integral of (sin(x)+sin(h)x)

\int (sin (x) + sin (h) x) d x

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

Solution steps

\int sin (x) + sin (h) x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (x) d x + \int sin (h) x d x

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

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

= - cos (x) + \frac{1}{2} x^{2} sin (h)

Add a constant to the solution

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

What is the integral of (sin(x)+sin(h)x) ?
The integral of (sin(x)+sin(h)x) is -cos(x)+1/2 x^2sin(h)+C