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Popular >

integral of x^3+x^2

Solution

\int x^{3} + x^{2} d x

Solution

\frac{x ^{4}}{4} + \frac{x ^{3}}{3} + C

Solution steps

\int x^{3} + x^{2} 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 x^{2} d x

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

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

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + C

Popular Examples

derivative of 4-sqrt(x^2+y^2)

\frac{d}{d x} (4 - x^{2} + y^{2})

integral of ((12x^4+3x^2+6ax)/(2x))

\int (\frac{12 x ^{4} + 3 x ^{2} + 6 a x}{2 x}) d x

limit as x approaches 3+of 7/(x-3)

x \to 3 + lim (\frac{7}{x - 3})

integral of (2x+4)/(x^2)

\int \frac{2 x + 4}{x ^{2}} d x

sum from n=0 to infinity of 1/((2^n))

n = 0 \sum \infty \frac{1}{( 2 ^{n} )}

Frequently Asked Questions (FAQ)

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