What is the integral of (u^{3/2}-3u+14) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (u^{3/2}-3u+14)

\int (u^{\frac{3}{2}} - 3 u + 14) d u

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

Solution steps

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

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

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

\int 14 d u = 14 u

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

Add a constant to the solution

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

\int [6 e^{u} - u^{3} (u + 1)] d u

\int 9 x x - 7 d x

\int (5 x - x) d x

\int (4 x^{3} + 6 x^{2} + 3) d x

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

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