What is the integral of 1/(\sqrt[5]{x)}+5/(e^{3x)} ?

The integral of 1/(\sqrt[5]{x)}+5/(e^{3x)} is 5/4 x^{4/5}-5/3 e^{-3x}+C

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integral of 1/(\sqrt[5]{x)}+5/(e^{3x)}

\frac{5}{4} x^{\frac{4}{5}} - \frac{5}{3} e^{- 3 x} + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int \frac{5}{e ^{3 x}} d x = - \frac{5}{3} e^{- 3 x}

= \frac{5}{4} x^{\frac{4}{5}} - \frac{5}{3} e^{- 3 x}

Add a constant to the solution

= \frac{5}{4} x^{\frac{4}{5}} - \frac{5}{3} e^{- 3 x} + C

What is the integral of 1/(\sqrt[5]{x)}+5/(e^{3x)} ?
The integral of 1/(\sqrt[5]{x)}+5/(e^{3x)} is 5/4 x^{4/5}-5/3 e^{-3x}+C