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Popular >

integral of x^3+4x

Solution

\int x^{3} + 4 x d x

Solution

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

Solution steps

\int x^{3} + 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^{3} d x + \int 4 x d x

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

Graph

Popular Examples

integral of sqrt(1/(x^4)-1/(x^2))

\int \frac{1}{x ^{4}} - \frac{1}{x ^{2}} d x

integral of e^{3x^4}

\int e^{3 x^{4}} d x

integral of 1/(x^2)sqrt(8+1/x)

\int \frac{1}{x ^{2}} 8 + \frac{1}{x} d x

integral of (x/(1+x))

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

integral of (5+9x)/(1+x^2)

\int \frac{5 + 9 x}{1 + x ^{2}} d x

Frequently Asked Questions (FAQ)

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