What is the integral of sqrt(u)(u^2+3u+7) ?

The integral of sqrt(u)(u^2+3u+7) is 2/7 u^{7/2}+6/5 u^{5/2}+14/3 u^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sqrt(u)(u^2+3u+7)

\int u (u^{2} + 3 u + 7) d u

\frac{2}{7} u^{\frac{7}{2}} + \frac{6}{5} u^{\frac{5}{2}} + \frac{14}{3} u^{\frac{3}{2}} + C

Solution steps

\int u (u^{2} + 3 u + 7) d u

Expand

u (u^{2} + 3 u + 7) : u^{\frac{5}{2}} + 3 u^{\frac{3}{2}} + 7 u

= \int u^{\frac{5}{2}} + 3 u^{\frac{3}{2}} + 7 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{5}{2}} d u + \int 3 u^{\frac{3}{2}} d u + \int 7 u d u

\int u^{\frac{5}{2}} d u = \frac{2}{7} u^{\frac{7}{2}}

\int 3 u^{\frac{3}{2}} d u = \frac{6}{5} u^{\frac{5}{2}}

\int 7 u d u = \frac{14}{3} u^{\frac{3}{2}}

= \frac{2}{7} u^{\frac{7}{2}} + \frac{6}{5} u^{\frac{5}{2}} + \frac{14}{3} u^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{7} u^{\frac{7}{2}} + \frac{6}{5} u^{\frac{5}{2}} + \frac{14}{3} u^{\frac{3}{2}} + C

\int x^{8} (x^{9} - 10)^{4} d x

\int sec^{2} (x) - cos (x) d x

\int (4 x^{2} + 3 + \frac{7}{x ^{2} + 1}) d x

\int \frac{sin ( 31 x )}{1 + cos ^{2} ( 31 x )} d x

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

What is the integral of sqrt(u)(u^2+3u+7) ?
The integral of sqrt(u)(u^2+3u+7) is 2/7 u^{7/2}+6/5 u^{5/2}+14/3 u^{3/2}+C