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Popular >

integral of 2e^x+x^2

Solution

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

Solution

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

Solution steps

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

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

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

= 2 e^{x} + \frac{x ^{3}}{3}

Add a constant to the solution

= 2 e^{x} + \frac{x ^{3}}{3} + C

Popular Examples

integral of 1/((2+sin(x)))

\int \frac{1}{( 2 + sin ( x ) )} d x

integral of (x^2)/((x-1)^{10)}

\int \frac{x ^{2}}{( x - 1 ) ^{10}} d x

integral of 1/(\sqrt[3]{y)+y}

integral of (x^3)/((x+3))

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

integral of 1/(sqrt((2-x^2)^3))

\int \frac{1}{( 2 - x ^{2} ) ^{3}} d x

Frequently Asked Questions (FAQ)

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