What is the integral of 7xsqrt(x+5) ?

The integral of 7xsqrt(x+5) is 7(2/5 (x+5)^{5/2}-10/3 (x+5)^{3/2})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7xsqrt(x+5)

\int 7 x x + 5 d x

7 (\frac{2}{5} (x + 5)^{\frac{5}{2}} - \frac{10}{3} (x + 5)^{\frac{3}{2}}) + C

Solution steps

\int 7 x x + 5 d x

Take the constant out:

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

= 7 \cdot \int x x + 5 d x

Apply u-substitution

: \int (u - 5) u d u

= 7 \cdot \int (u - 5) u d u

Expand

(u - 5) u : u^{\frac{3}{2}} - 5 u

= 7 \cdot \int u^{\frac{3}{2}} - 5 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

= 7 (\int u^{\frac{3}{2}} d u - \int 5 u d u)

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int 5 u d u = \frac{10}{3} u^{\frac{3}{2}}

= 7 (\frac{2}{5} u^{\frac{5}{2}} - \frac{10}{3} u^{\frac{3}{2}})

Substitute back

u = x + 5

= 7 (\frac{2}{5} (x + 5)^{\frac{5}{2}} - \frac{10}{3} (x + 5)^{\frac{3}{2}})

Add a constant to the solution

= 7 (\frac{2}{5} (x + 5)^{\frac{5}{2}} - \frac{10}{3} (x + 5)^{\frac{3}{2}}) + C

\int \frac{1}{2 cos ^{2} ( 3 x )} d x

\int x^{\frac{1}{10}} d x

\int 3 x^{5} - x^{2} + 4 x - 1 d x

\int \frac{1}{1 + e ^{x} + e ^{- x}} d x

\int \frac{x ln ^{5} ( x ^{2} + 3 )}{x ^{2} + 3} d x

What is the integral of 7xsqrt(x+5) ?
The integral of 7xsqrt(x+5) is 7(2/5 (x+5)^{5/2}-10/3 (x+5)^{3/2})+C