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

The integral from 0 to 3 of e^{x/3}(x^2+2x) is 27e-36

Popular >

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

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

27 e - 36

Decimal Notation

37.39360 \dots

Solution steps

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

Expand

e^{\frac{x}{3}} (x^{2} + 2 x) : e^{\frac{x}{3}} x^{2} + 2 e^{\frac{x}{3}} x

= \int_{0}^{3} e^{\frac{x}{3}} x^{2} + 2 e^{\frac{x}{3}} 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_{0}^{3} e^{\frac{x}{3}} x^{2} d x + \int_{0}^{3} 2 e^{\frac{x}{3}} x d x

\int_{0}^{3} e^{\frac{x}{3}} x^{2} d x = 27 e - 54

\int_{0}^{3} 2 e^{\frac{x}{3}} x d x = 18

= 27 e - 54 + 18

Simplify

= 27 e - 36

\int_{- 2}^{2} \frac{8}{4 + x ^{2}} d x

\int_{2}^{4} (x^{2} + 2 x) d x

\int_{- 1}^{0} - x cos (nπ x) d x

\int_{2}^{6} 2 x^{2} + 4 d x

\int_{- 2}^{4} x^{2} d x

What is the integral from 0 to 3 of e^{x/3}(x^2+2x) ?
The integral from 0 to 3 of e^{x/3}(x^2+2x) is 27e-36