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Popular >

integral of 2+xe^x

Solution

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

Solution

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

Solution steps

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

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

Popular Examples

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

\int (2 x - 1) (2 x + 3) d x

integral of (8x^3-9/x+4e^x)

\int (8 x^{3} - \frac{9}{x} + 4 e^{x}) d x

integral of (x^2+2)^{1/2}

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

integral of xcsc^2(a)x

\int x csc^{2} (a) x d x

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

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

Frequently Asked Questions (FAQ)

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