What is the integral from 0 to ln(3) of e^x(1+e^x)^2 ?

The integral from 0 to ln(3) of e^x(1+e^x)^2 is 56/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to ln(3) of e^x(1+e^x)^2

\int_{0}^{l n (3)} e^{x} (1 + e^{x})^{2} d x

\frac{56}{3}

Decimal

18.66666 \dots

Solution steps

\int_{0}^{l n (3)} e^{x} (1 + e^{x})^{2} d x

Apply u-substitution

: \int_{2}^{4} u^{2} d u

= \int_{2}^{4} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{2}^{4}

= [\frac{u ^{3}}{3}]_{2}^{4}

Compute the boundaries:

\frac{56}{3}

= \frac{56}{3}

\int_{- 1}^{2} (x^{3} + e^{\frac{1}{4} x}) d x

\int_{0}^{\infty} e^{- 0.1 t} d t

\int_{2}^{5} x^{4} - 2 x d x

\int_{1}^{2} (3 x^{2} + 3) d x

\int_{0}^{3} (8 x - 2 x^{3}) d x

What is the integral from 0 to ln(3) of e^x(1+e^x)^2 ?
The integral from 0 to ln(3) of e^x(1+e^x)^2 is 56/3