What is the integral of xsqrt(x+14) ?

The integral of xsqrt(x+14) is 2/5 (x+14)^{5/2}-28/3 (x+14)^{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 xsqrt(x+14)

\int x x + 14 d x

\frac{2}{5} (x + 14)^{\frac{5}{2}} - \frac{28}{3} (x + 14)^{\frac{3}{2}} + C

Solution steps

\int x x + 14 d x

Apply u-substitution

: \int (u - 14) u d u

= \int (u - 14) u d u

Expand

(u - 14) u : u^{\frac{3}{2}} - 14 u

= \int u^{\frac{3}{2}} - 14 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

= \int u^{\frac{3}{2}} d u - \int 14 u d u

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

\int 14 u d u = \frac{28}{3} u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} - \frac{28}{3} u^{\frac{3}{2}}

Substitute back

u = x + 14

= \frac{2}{5} (x + 14)^{\frac{5}{2}} - \frac{28}{3} (x + 14)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} (x + 14)^{\frac{5}{2}} - \frac{28}{3} (x + 14)^{\frac{3}{2}} + C

\frac{d}{d x} (m x^{m + 5} + 6 x^{m} y^{n} + n x^{n + 3})

\int ln (x) (x^{2}) d x

\int sec (2 θ) d θ

f (x) = 4 x^{2} - 2 x + 5

(sec^{2} (x))^{^{'}}

What is the integral of xsqrt(x+14) ?
The integral of xsqrt(x+14) is 2/5 (x+14)^{5/2}-28/3 (x+14)^{3/2}+C