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

The integral of sqrt(x)+sin(x) is 2/3 x^{3/2}-cos(x)+C

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integral of sqrt(x)+sin(x)

\int x + sin (x) d x

\frac{2}{3} x^{\frac{3}{2}} - cos (x) + C

Solution steps

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

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

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

= \frac{2}{3} x^{\frac{3}{2}} - cos (x)

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - cos (x) + C

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What is the integral of sqrt(x)+sin(x) ?
The integral of sqrt(x)+sin(x) is 2/3 x^{3/2}-cos(x)+C