What is the integral of (3x\sqrt[3]{x^2+2}+e^{5x}) ?

The integral of (3x\sqrt[3]{x^2+2}+e^{5x}) is 9/8 (x^2+2)^{4/3}+1/5 e^{5x}+C

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integral of (3x\sqrt[3]{x^2+2}+e^{5x})

\frac{9}{8} (x^{2} + 2)^{\frac{4}{3}} + \frac{1}{5} e^{5 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 e^{5 x} d x = \frac{1}{5} e^{5 x}

= \frac{9}{8} (x^{2} + 2)^{\frac{4}{3}} + \frac{1}{5} e^{5 x}

Add a constant to the solution

= \frac{9}{8} (x^{2} + 2)^{\frac{4}{3}} + \frac{1}{5} e^{5 x} + C

x + \frac{2}{x}

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ln (3 x + 1)

What is the integral of (3x\sqrt[3]{x^2+2}+e^{5x}) ?
The integral of (3x\sqrt[3]{x^2+2}+e^{5x}) is 9/8 (x^2+2)^{4/3}+1/5 e^{5x}+C