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

The integral of (1-x^2)/(sqrt(x)) is 2sqrt(x)-2/5 x^{5/2}+C

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integral of (1-x^2)/(sqrt(x))

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

2 x - \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

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

Expand

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

= \int \frac{1}{x} - x^{\frac{3}{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 \frac{1}{x} d x - \int x^{\frac{3}{2}} d x

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= 2 x - \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 2 x - \frac{2}{5} x^{\frac{5}{2}} + C

x \to 0 + lim (cos (x))

y^{^{''}} + 0.2 x^{2} - 0.35 x = 0

n = 1 \sum \infty \frac{1}{2 ^{3 n}}

f (x) = \frac{1}{2 x + 3}, at x = 2

\frac{d}{d x} (y cos (x))

What is the integral of (1-x^2)/(sqrt(x)) ?
The integral of (1-x^2)/(sqrt(x)) is 2sqrt(x)-2/5 x^{5/2}+C