What is the integral of e^{4x}+2x^{1/4} ?

The integral of e^{4x}+2x^{1/4} is 1/4 e^{4x}+8/5 x^{5/4}+C

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integral of e^{4x}+2x^{1/4}

\int e^{4 x} + 2 x^{\frac{1}{4}} d x

\frac{1}{4} e^{4 x} + \frac{8}{5} x^{\frac{5}{4}} + C

Solution steps

\int e^{4 x} + 2 x^{\frac{1}{4}} 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 2 x^{\frac{1}{4}} d x

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

\int 2 x^{\frac{1}{4}} d x = \frac{8}{5} x^{\frac{5}{4}}

= \frac{1}{4} e^{4 x} + \frac{8}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{1}{4} e^{4 x} + \frac{8}{5} x^{\frac{5}{4}} + C

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What is the integral of e^{4x}+2x^{1/4} ?
The integral of e^{4x}+2x^{1/4} is 1/4 e^{4x}+8/5 x^{5/4}+C