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Popular >

integral of x^2-e^x

Solution

\int x^{2} - e^{x} d x

Solution

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

Solution steps

\int x^{2} - e^{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^{2} d x - \int e^{x} d x

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

\int e^{x} d x = e^{x}

= \frac{x ^{3}}{3} - e^{x}

Add a constant to the solution

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

Graph

Popular Examples

integral of cot^2(t)

\int cot^{2} (t) d t

integral of 1/4 x^3+3x^2-3/4 x+4

\int \frac{1}{4} x^{3} + 3 x^{2} - \frac{3}{4} x + 4 d x

integral of sqrt(8x+7)

\int 8 x + 7 d x

integral of (2x+13)/(x^2+3x-4)

\int \frac{2 x + 13}{x ^{2} + 3 x - 4} d x

integral of (2e^x+3/(2x)-2x^{-2})

\int (2 e^{x} + \frac{3}{2 x} - 2 x^{- 2}) d x

Frequently Asked Questions (FAQ)

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