What is the integral from 0 to 1 of 3e^x-3xe^{x^2} ?

The integral from 0 to 1 of 3e^x-3xe^{x^2} is 3(e-1)-(3(e-1))/2

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integral from 0 to 1 of 3e^x-3xe^{x^2}

\int_{0}^{1} 3 e^{x} - 3 x e^{x^{2}} d x

3 (e - 1) - \frac{3 ( e - 1 )}{2}

Decimal

2.57742 \dots

Solution steps

\int_{0}^{1} 3 e^{x} - 3 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_{0}^{1} 3 e^{x} d x - \int_{0}^{1} 3 x e^{x^{2}} d x

\int_{0}^{1} 3 e^{x} d x = 3 (e - 1)

\int_{0}^{1} 3 x e^{x^{2}} d x = \frac{3 ( e - 1 )}{2}

= 3 (e - 1) - \frac{3 ( e - 1 )}{2}

\int \frac{( u )}{( u + 1 ) ( u - 1 )} d u

\frac{d}{d x} (e^{3 x^{3} - x})

x^{4} - x^{3} + 2

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

\frac{2 x + 9}{x}

What is the integral from 0 to 1 of 3e^x-3xe^{x^2} ?
The integral from 0 to 1 of 3e^x-3xe^{x^2} is 3(e-1)-(3(e-1))/2