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Popular >

integral of (x^3+x)/x

Solution

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

Solution

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

Solution steps

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

Simplify

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

= \int x^{2} + 1 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^{2} d x + \int 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

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slope ofintercept (-5,1),(-4,-9)slope intercept

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Frequently Asked Questions (FAQ)

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