What is the integral of (x^{3/4}-1/(x^{3/4)}) ?

The integral of (x^{3/4}-1/(x^{3/4)}) is 4/7 x^{7/4}-4x^{1/4}+C

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integral of (x^{3/4}-1/(x^{3/4)})

\int (x^{\frac{3}{4}} - \frac{1}{x ^{\frac{3}{4}}}) d x

\frac{4}{7} x^{\frac{7}{4}} - 4 x^{\frac{1}{4}} + C

Solution steps

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

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

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

= \frac{4}{7} x^{\frac{7}{4}} - 4 x^{\frac{1}{4}}

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{4}} - 4 x^{\frac{1}{4}} + C

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What is the integral of (x^{3/4}-1/(x^{3/4)}) ?
The integral of (x^{3/4}-1/(x^{3/4)}) is 4/7 x^{7/4}-4x^{1/4}+C