What is the integral of (1+20w)sqrt(w) ?

The integral of (1+20w)sqrt(w) is 2/3 w^{3/2}(1+20w)-16/3 w^{5/2}+C

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integral of (1+20w)sqrt(w)

\int (1 + 20 w) w d w

\frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \frac{16}{3} w^{\frac{5}{2}} + C

Solution steps

\int (1 + 20 w) w d w

Apply Integration By Parts

: \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \int \frac{40}{3} w^{\frac{3}{2}} d w

= \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \int \frac{40}{3} w^{\frac{3}{2}} d w

\int \frac{40}{3} w^{\frac{3}{2}} d w = \frac{16}{3} w^{\frac{5}{2}}

= \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \frac{16}{3} w^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \frac{16}{3} w^{\frac{5}{2}} + C

\int \frac{x ^{2}}{( 16 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (e^{3 x} \cdot 3)

\int cos (6 y) - cos (- 6 y) d y

\frac{d}{d x} (\frac{1}{3 x + 6})

(\frac{1}{1 - 2 x})^{3}

What is the integral of (1+20w)sqrt(w) ?
The integral of (1+20w)sqrt(w) is 2/3 w^{3/2}(1+20w)-16/3 w^{5/2}+C