What is the integral of (7-1/(x^4))sqrt(\sqrt{x)} ?

The integral of (7-1/(x^4))sqrt(\sqrt{x)} is 4/5 x^{5/4}(7-1/(x^4))+(64)/(55x^{11/4)}+C

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integral of (7-1/(x^4))sqrt(\sqrt{x)}

\int (7 - \frac{1}{x ^{4}}) x d x

\frac{4}{5} x^{\frac{5}{4}} (7 - \frac{1}{x ^{4}}) + \frac{64}{55 x ^{\frac{11}{4}}} + C

Solution steps

\int (7 - \frac{1}{x ^{4}}) x d x

Apply Integration By Parts

: \frac{4}{5} x^{\frac{5}{4}} (7 - \frac{1}{x ^{4}}) - \int \frac{16}{5 x ^{\frac{15}{4}}} d x

= \frac{4}{5} x^{\frac{5}{4}} (7 - \frac{1}{x ^{4}}) - \int \frac{16}{5 x ^{\frac{15}{4}}} d x

\int \frac{16}{5 x ^{\frac{15}{4}}} d x = - \frac{64}{55 x ^{\frac{11}{4}}}

= \frac{4}{5} x^{\frac{5}{4}} (7 - \frac{1}{x ^{4}}) - (- \frac{64}{55 x ^{\frac{11}{4}}})

Simplify

= \frac{4}{5} x^{\frac{5}{4}} (7 - \frac{1}{x ^{4}}) + \frac{64}{55 x ^{\frac{11}{4}}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{4}} (7 - \frac{1}{x ^{4}}) + \frac{64}{55 x ^{\frac{11}{4}}} + C

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What is the integral of (7-1/(x^4))sqrt(\sqrt{x)} ?
The integral of (7-1/(x^4))sqrt(\sqrt{x)} is 4/5 x^{5/4}(7-1/(x^4))+(64)/(55x^{11/4)}+C