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

The integral of (u+3sqrt(u)-2u^3) is (u^2)/2+2u^{3/2}-(u^4)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{u ^{2}}{2} + 2 u^{\frac{3}{2}} - \frac{u ^{4}}{2} + C

Solution steps

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

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

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

\int 2 u^{3} d u = \frac{u ^{4}}{2}

= \frac{u ^{2}}{2} + 2 u^{\frac{3}{2}} - \frac{u ^{4}}{2}

Add a constant to the solution

= \frac{u ^{2}}{2} + 2 u^{\frac{3}{2}} - \frac{u ^{4}}{2} + C

\int \frac{5 x}{3 x ^{2} - 5} d x

\int z 1 - z^{2} d z

\int - sin (x) sec^{3} (x) d x

\int \frac{x ^{3} + 3 x ^{2} - 9 x - 2}{x - 2} d x

\int \frac{1 + x}{x} \frac{1}{x} d x

What is the integral of (u+3sqrt(u)-2u^3) ?
The integral of (u+3sqrt(u)-2u^3) is (u^2)/2+2u^{3/2}-(u^4)/2+C