What is the integral of (x^3+1/(xsqrt(x))) ?

The integral of (x^3+1/(xsqrt(x))) is (x^4)/4-2/(sqrt(x))+C

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integral of (x^3+1/(xsqrt(x)))

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

\frac{x ^{4}}{4} - \frac{2}{x} + C

Solution steps

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

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

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

= \frac{x ^{4}}{4} - \frac{2}{x}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{2}{x} + C

What is the integral of (x^3+1/(xsqrt(x))) ?
The integral of (x^3+1/(xsqrt(x))) is (x^4)/4-2/(sqrt(x))+C