What is the integral of (3x+4)/(\sqrt[5]{x)} ?

The integral of (3x+4)/(\sqrt[5]{x)} is 5/3 x^{9/5}+5x^{4/5}+C

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integral of (3x+4)/(\sqrt[5]{x)}

\frac{5}{3} x^{\frac{9}{5}} + 5 x^{\frac{4}{5}} + C

Solution steps

Expand

Apply the Sum Rule:

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

\int 3 x^{\frac{4}{5}} d x = \frac{5}{3} x^{\frac{9}{5}}

= \frac{5}{3} x^{\frac{9}{5}} + 5 x^{\frac{4}{5}}

Add a constant to the solution

= \frac{5}{3} x^{\frac{9}{5}} + 5 x^{\frac{4}{5}} + C

\int 2 z x e^{- x^{2}} d x

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

\int \frac{2 sin ( x )}{e ^{2 x}} d x

\int cos (5 - 4 x) d x

What is the integral of (3x+4)/(\sqrt[5]{x)} ?
The integral of (3x+4)/(\sqrt[5]{x)} is 5/3 x^{9/5}+5x^{4/5}+C