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Popular >

integral of xex^2-1

Solution

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

Solution

\frac{e x ^{4}}{4} - x + C

Solution steps

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

\int x e x^{2} d x = \frac{e x ^{4}}{4}

\int 1 d x = x

= \frac{e x ^{4}}{4} - x

Add a constant to the solution

= \frac{e x ^{4}}{4} - x + C

Popular Examples

integral of sin^4(7θ)

\int sin^{4} (7 θ) d θ

integral of (x^4)/(x^2+225)

\int \frac{x ^{4}}{x ^{2} + 225} d x

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\int e^{6 x} (x^{2} - 11 x + 1) d x

integral of ln|1-x|

\int ln ∣ 1 - x ∣ d x

integral of 2/(sqrt(5-5x^2))

\int \frac{2}{5 - 5 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of xex^2-1 ?
The integral of xex^2-1 is (ex^4)/4-x+C