What is the integral of e^{4x}+xsqrt(x) ?

The integral of e^{4x}+xsqrt(x) is 1/4 e^{4x}+2/5 x^{5/2}+C

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integral of e^{4x}+xsqrt(x)

\int e^{4 x} + x x d x

\frac{1}{4} e^{4 x} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int e^{4 x} + 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 e^{4 x} d x + \int x x d x

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

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

= \frac{1}{4} e^{4 x} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{4} e^{4 x} + \frac{2}{5} x^{\frac{5}{2}} + C

What is the integral of e^{4x}+xsqrt(x) ?
The integral of e^{4x}+xsqrt(x) is 1/4 e^{4x}+2/5 x^{5/2}+C