What is the integral of (xsqrt(x)+\sqrt[4]{x})/(x^2) ?

The integral of (xsqrt(x)+\sqrt[4]{x})/(x^2) is 2sqrt(x)-4/(3x^{3/4)}+C

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integral of (xsqrt(x)+\sqrt[4]{x})/(x^2)

2 x - \frac{4}{3 x ^{\frac{3}{4}}} + C

Solution steps

Expand

= \int \frac{1}{x} + \frac{1}{x ^{\frac{7}{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 \frac{1}{x} d x + \int \frac{1}{x ^{\frac{7}{4}}} d x

\int \frac{1}{x} d x = 2 x

\int \frac{1}{x ^{\frac{7}{4}}} d x = - \frac{4}{3 x ^{\frac{3}{4}}}

= 2 x - \frac{4}{3 x ^{\frac{3}{4}}}

Add a constant to the solution

= 2 x - \frac{4}{3 x ^{\frac{3}{4}}} + C

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What is the integral of (xsqrt(x)+\sqrt[4]{x})/(x^2) ?
The integral of (xsqrt(x)+\sqrt[4]{x})/(x^2) is 2sqrt(x)-4/(3x^{3/4)}+C