What is the integral of (1+30w)sqrt(w) ?

The integral of (1+30w)sqrt(w) is 2/3 w^{3/2}+12w^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1+30w)sqrt(w)

\int (1 + 30 w) w d w

\frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}} + C

Solution steps

\int (1 + 30 w) w d w

Apply Integration By Parts

: \frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - \int 20 w^{\frac{3}{2}} d w

= \frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - \int 20 w^{\frac{3}{2}} d w

\int 20 w^{\frac{3}{2}} d w = 8 w^{\frac{5}{2}}

= \frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - 8 w^{\frac{5}{2}}

Simplify

\frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - 8 w^{\frac{5}{2}} : \frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}}

= \frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}} + C

\int 1 - x^{2} d x

f (x) = 6 x + 8

\frac{d}{d x} (arctan (7 x^{2} - 1))

e^{3 - x}

What is the integral of (1+30w)sqrt(w) ?
The integral of (1+30w)sqrt(w) is 2/3 w^{3/2}+12w^{5/2}+C