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Popular >

integral of (x^2+x)/x

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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