What is the integral of (sqrt(x^3)-3/(1+x^2)) ?

The integral of (sqrt(x^3)-3/(1+x^2)) is 2/5 x^{5/2}-3arctan(x)+C

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integral of (sqrt(x^3)-3/(1+x^2))

\int (x^{3} - \frac{3}{1 + x ^{2}}) d x

\frac{2}{5} x^{\frac{5}{2}} - 3 arctan (x) + C

Solution steps

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

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

\int \frac{3}{1 + x ^{2}} d x = 3 arctan (x)

= \frac{2}{5} x^{\frac{5}{2}} - 3 arctan (x)

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - 3 arctan (x) + C

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What is the integral of (sqrt(x^3)-3/(1+x^2)) ?
The integral of (sqrt(x^3)-3/(1+x^2)) is 2/5 x^{5/2}-3arctan(x)+C