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Popular >

integral of xe^x+2

Solution

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

Solution

e^{x} x - e^{x} + 2 x + C

Solution steps

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

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

\int 2 d x = 2 x

= e^{x} x - e^{x} + 2 x

Add a constant to the solution

= e^{x} x - e^{x} + 2 x + C

Graph

Popular Examples

integral of (20)/(x^3)

\int \frac{20}{x ^{3}} d x

integral of 2/(3+cos(x))

\int \frac{2}{3 + cos ( x )} d x

integral of 1/(x^2)*cos(1/x)

\int \frac{1}{x ^{2}} \cdot cos (\frac{1}{x}) d x

integral of (x*2^x)

\int (x \cdot 2^{x}) d x

integral of (1/(x^2+a^2))

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

Frequently Asked Questions (FAQ)

What is the integral of xe^x+2 ?
The integral of xe^x+2 is e^xx-e^x+2x+C