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

The integral from 0 to 1 of xe^{2x} is (e^2+1)/4

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 xe^{2x}

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

\frac{e ^{2} + 1}{4}

Decimal Notation

2.09726 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{2} \frac{e ^{u} u}{4} d u

= \int_{0}^{2} \frac{e ^{u} u}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{0}^{2} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{0}^{2}

= \frac{1}{4} [e^{u} u - \int e^{u} d u]_{0}^{2}

\int e^{u} d u = e^{u}

= \frac{1}{4} [e^{u} u - e^{u}]_{0}^{2}

Compute the boundaries:

e^{2} + 1

= \frac{1}{4} (e^{2} + 1)

Simplify

= \frac{e ^{2} + 1}{4}

y^{^{'}} + 4 y = 6

- 6.25 t^{2} + 50 t

(x^{2} + 4 x y) d x + x d y = 0

x \to 1 lim (\frac{5}{( x - 1 ) ^{2}})

\frac{d}{d x} ((1 + 2 x + 3 x^{2} + 4 x^{3})^{100})

What is the integral from 0 to 1 of xe^{2x} ?
The integral from 0 to 1 of xe^{2x} is (e^2+1)/4