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Popular >

integral of (x^3+x^2)/x

Solution

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

Solution

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + C

Solution steps

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

Expand

\frac{x ^{3} + x ^{2}}{x} : \frac{x ^{3}}{x} + \frac{x ^{2}}{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{x ^{3}}{x} d x + \int \frac{x ^{2}}{x} d x

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

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

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + C

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integral of e^w

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Frequently Asked Questions (FAQ)

What is the integral of (x^3+x^2)/x ?
The integral of (x^3+x^2)/x is (x^3)/3+(x^2)/2+C