What is the integral of (sin(x)+2e^x-3xsqrt(x)) ?

The integral of (sin(x)+2e^x-3xsqrt(x)) is -cos(x)+2e^x-6/5 x^{5/2}+C

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integral of (sin(x)+2e^x-3xsqrt(x))

\int (sin (x) + 2 e^{x} - 3 x x) d x

- cos (x) + 2 e^{x} - \frac{6}{5} x^{\frac{5}{2}} + C

Solution steps

\int sin (x) + 2 e^{x} - 3 x 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 2 e^{x} d x - \int 3 x x d x

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

\int 2 e^{x} d x = 2 e^{x}

\int 3 x x d x = \frac{6}{5} x^{\frac{5}{2}}

= - cos (x) + 2 e^{x} - \frac{6}{5} x^{\frac{5}{2}}

Add a constant to the solution

= - cos (x) + 2 e^{x} - \frac{6}{5} x^{\frac{5}{2}} + C

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What is the integral of (sin(x)+2e^x-3xsqrt(x)) ?
The integral of (sin(x)+2e^x-3xsqrt(x)) is -cos(x)+2e^x-6/5 x^{5/2}+C