What is the integral of \sqrt[4]{x^3}+7/x ?

The integral of \sqrt[4]{x^3}+7/x is 4/7 x^{7/4}+7ln|x|+C

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integral of \sqrt[4]{x^3}+7/x

\frac{4}{7} x^{\frac{7}{4}} + 7 ln ∣ 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{7}{x} d x = 7 ln ∣ x ∣

= \frac{4}{7} x^{\frac{7}{4}} + 7 ln ∣ x ∣

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{4}} + 7 ln ∣ x ∣ + C

What is the integral of \sqrt[4]{x^3}+7/x ?
The integral of \sqrt[4]{x^3}+7/x is 4/7 x^{7/4}+7ln|x|+C