What is the integral of (1-1/(x^2))sqrt(x\sqrt{x)} ?

The integral of (1-1/(x^2))sqrt(x\sqrt{x)} is 4/7 x^{7/4}+4/(\sqrt[4]{x)}+C

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integral of (1-1/(x^2))sqrt(x\sqrt{x)}

\int (1 - \frac{1}{x ^{2}}) x x d x

Solution steps

\int (1 - \frac{1}{x ^{2}}) x x d x

Expand

(1 - \frac{1}{x ^{2}}) x x : x^{\frac{3}{2}} - \frac{x ^{\frac{3}{2}}}{x ^{2}}

= \int x^{\frac{3}{2}} - \frac{x ^{\frac{3}{2}}}{x ^{2}} 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}{2}} d x - \int \frac{x ^{\frac{3}{2}}}{x ^{2}} d x

\int x^{\frac{3}{2}} d x = \frac{4}{7} x^{\frac{7}{4}}

Simplify

Add a constant to the solution

\frac{d}{d x} (3 x^{2} - y^{2})

\int sec (t) sec (t) + tan (t) d t

\int_{0}^{\infty} e^{- ∣ x ∣} d x

\frac{d}{d x} ((3 x^{2} - 9)^{- 12})

y = 2^{x}

What is the integral of (1-1/(x^2))sqrt(x\sqrt{x)} ?
The integral of (1-1/(x^2))sqrt(x\sqrt{x)} is 4/7 x^{7/4}+4/(\sqrt[4]{x)}+C