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

The integral from 0 to 3 of (3e^{2x}-x^2) is (3(e^6-1))/2-9

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integral from 0 to 3 of (3e^{2x}-x^2)

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

\frac{3 ( e ^{6} - 1 )}{2} - 9

Decimal Notation

594.64319 \dots

Solution steps

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

\int_{0}^{3} 3 e^{2 x} d x = \frac{3 ( e ^{6} - 1 )}{2}

\int_{0}^{3} x^{2} d x = 9

= \frac{3 ( e ^{6} - 1 )}{2} - 9

\int_{0}^{1} 2 y e^{y} d y

\int_{- 1}^{2} ((2 - x^{2}) - (- x)) d x

\int_{1}^{9} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

\int_{0}^{t} 3 t^{3} d t

\int_{- 3}^{2} - x^{2} d x

What is the integral from 0 to 3 of (3e^{2x}-x^2) ?
The integral from 0 to 3 of (3e^{2x}-x^2) is (3(e^6-1))/2-9