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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

\int y^{2} (\frac{1}{y ^{5}} + \frac{y ^{4}}{2}) d y

6 x arcsin (x)

(t + e^{t}) (9 - t)

3 y^{^{'''}} + 12 y^{^{''}} + 12 y^{^{'}} = 0

\int_{0}^{1} (x^{2} + x) e^{x} d x

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