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Popular >

integral of xe^x+2e^x

Solution

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

Solution

e^{x} x + e^{x} + C

Solution steps

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

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

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

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

Simplify

= e^{x} x + e^{x}

Add a constant to the solution

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

Popular Examples

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

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

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

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

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

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

integral of 5sin(4x)

\int 5 sin (4 x) d x

integral of 2e^{1/2 x}

\int 2 e^{\frac{1}{2} x} d x

Frequently Asked Questions (FAQ)

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