What is the integral from 1 to 4 of 3xsqrt(x+1) ?

The integral from 1 to 4 of 3xsqrt(x+1) is 3(10sqrt(5)+(-4sqrt(2)-50sqrt(5))/(15))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 4 of 3xsqrt(x+1)

\int_{1}^{4} 3 x x + 1 d x

3 (105 + \frac{- 4 2 - 50 5}{15})

Decimal

43.58998 \dots

Solution steps

\int_{1}^{4} 3 x x + 1 d x

Take the constant out:

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

= 3 \cdot \int_{1}^{4} x x + 1 d x

Apply u-substitution

= 3 \cdot \int_{2}^{5} (u - 1) u d u

Expand

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

= 3 \cdot \int_{2}^{5} 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

= 3 (\int_{2}^{5} u^{\frac{3}{2}} d u - \int_{2}^{5} u d u)

\int_{2}^{5} u^{\frac{3}{2}} d u = 105 - \frac{8 2}{5}

\int_{2}^{5} u d u = \frac{10 5 - 4 2}{3}

= 3 (105 - \frac{8 2}{5} - \frac{10 5 - 4 2}{3})

Join

105 - \frac{8 2}{5} - \frac{10 5 - 4 2}{3} : 105 + \frac{- 4 2 - 50 5}{15}

= 3 (105 + \frac{- 4 2 - 50 5}{15})

What is the integral from 1 to 4 of 3xsqrt(x+1) ?
The integral from 1 to 4 of 3xsqrt(x+1) is 3(10sqrt(5)+(-4sqrt(2)-50sqrt(5))/(15))