What is the integral of 10wsqrt(w) ?

The integral of 10wsqrt(w) is 4w^{5/2}+C

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integral of 10wsqrt(w)

\int 10 w w d w

4 w^{\frac{5}{2}} + C

Solution steps

\int 10 w w d w

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int w w d w

Simplify

w w : w^{\frac{3}{2}}

= 10 \cdot \int w^{\frac{3}{2}} d w

Apply the Power Rule

: \frac{2}{5} w^{\frac{5}{2}}

= 10 \cdot \frac{2}{5} w^{\frac{5}{2}}

Simplify

10 \cdot \frac{2}{5} w^{\frac{5}{2}} : 4 w^{\frac{5}{2}}

= 4 w^{\frac{5}{2}}

Add a constant to the solution

= 4 w^{\frac{5}{2}} + C

f (x) = (x + 2) e^{\frac{1}{x}}

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

y^{^{'}} = e^{y - x}

\frac{d}{d x} (\frac{( x ^{2} + 4 )}{x ^{2} - 4})

\frac{sec ( x )}{1 + sec ( x )}