What is the integral from 0 to 1 of (3x^e+5e^x) ?

The integral from 0 to 1 of (3x^e+5e^x) is 3/(e+1)+5(e-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of (3x^e+5e^x)

\int_{0}^{1} (3 x^{e} + 5 e^{x}) d x

\frac{3}{e + 1} + 5 (e - 1)

Decimal

9.39823 \dots

Solution steps

\int_{0}^{1} 3 x^{e} + 5 e^{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}^{1} 3 x^{e} d x + \int_{0}^{1} 5 e^{x} d x

\int_{0}^{1} 3 x^{e} d x = \frac{3}{e + 1}

\int_{0}^{1} 5 e^{x} d x = 5 (e - 1)

= \frac{3}{e + 1} + 5 (e - 1)

\int_{0}^{2} y^{2} - 2 y d y

\int_{2}^{10} (\frac{1}{x}) d x

\int_{- 3}^{2} 6 x - x^{2} - x^{3} d x

\int_{2}^{6} 5 x d x

\int_{\frac{1}{2}}^{2} \frac{2}{x} d x

What is the integral from 0 to 1 of (3x^e+5e^x) ?
The integral from 0 to 1 of (3x^e+5e^x) is 3/(e+1)+5(e-1)