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Popular >

integral of (x+x^3)

Solution

\int (x + x^{3}) d x

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (7sin(x))/(cos^2(x))

\int \frac{7 sin ( x )}{cos ^{2} ( x )} d x

integral of (a-x)sqrt(a+x)

\int (a - x) a + x d x

integral of e^{3x}+5e^{-x}

\int e^{3 x} + 5 e^{- x} d x

integral of (ln(1-x))

\int (ln (1 - x)) d x

integral of e^{8x-4}

\int e^{8 x - 4} d x

Frequently Asked Questions (FAQ)

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