What is the integral from 0 to 4 of xsqrt(2x+1) ?

The integral from 0 to 4 of xsqrt(2x+1) is 298/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 4 of xsqrt(2x+1)

\int_{0}^{4} x 2 x + 1 d x

\frac{298}{15}

Decimal Notation

19.86666 \dots

Solution steps

\int_{0}^{4} x 2 x + 1 d x

Apply u-substitution

: \int_{1}^{9} \frac{u ( u - 1 )}{4} d u

= \int_{1}^{9} \frac{u ( u - 1 )}{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_{1}^{9} u (u - 1) d u

Expand

u (u - 1) : u^{\frac{3}{2}} - u

= \frac{1}{4} \cdot \int_{1}^{9} u^{\frac{3}{2}} - u d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{4} (\int_{1}^{9} u^{\frac{3}{2}} d u - \int_{1}^{9} u d u)

\int_{1}^{9} u^{\frac{3}{2}} d u = \frac{484}{5}

\int_{1}^{9} u d u = \frac{52}{3}

= \frac{1}{4} (\frac{484}{5} - \frac{52}{3})

Simplify

\frac{1}{4} (\frac{484}{5} - \frac{52}{3}) : \frac{298}{15}

= \frac{298}{15}

\frac{( 8 x ^{3} - 4 x ^{2} + 3 )}{x}

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

\int (x^{7} + 1) e^{x^{8} + 8 x} d x

\int \frac{( e ^{- x} )}{x} d x

What is the integral from 0 to 4 of xsqrt(2x+1) ?
The integral from 0 to 4 of xsqrt(2x+1) is 298/15