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Popular Calculus >

integral of x^4+x

Solution

\int x^{4} + x d x

Solution

\frac{x ^{5}}{5} + \frac{x ^{2}}{2} + C

Solution steps

\int x^{4} + 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^{4} d x + \int x d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

= \frac{x ^{5}}{5} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{x ^{2}}{2} + C

Graph

Popular Examples

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integral of 1/(cos^5(x)sin(x))

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integral of 8sqrt(1+x^4)

Frequently Asked Questions (FAQ)

What is the integral of x^4+x ?
The integral of x^4+x is (x^5)/5+(x^2)/2+C