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Popular >

integral of xe^x-1

Solution

\int x e^{x} - 1 d x

Solution

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

Solution steps

\int x e^{x} - 1 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 1 d x

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

\int 1 d x = x

= e^{x} x - e^{x} - x

Add a constant to the solution

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

Graph

Popular Examples

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\int x (x^{2} + 8)^{5} d x

integral of 4x(2x-1)(4x+1)

\int 4 x (2 x - 1) (4 x + 1) d x

integral of (x^3)/(\sqrt[3]{1+x^4)}

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

integral of 1/(x(4-x^2))

\int \frac{1}{x ( 4 - x ^{2} )} d x

Frequently Asked Questions (FAQ)

What is the integral of xe^x-1 ?
The integral of xe^x-1 is e^xx-e^x-x+C