What is the integral of 10x*sqrt(x) ?

The integral of 10x*sqrt(x) is 4x^{5/2}+C

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integral of 10x*sqrt(x)

\int 10 x \cdot x d x

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

Solution steps

\int 10 x x d x

Take the constant out:

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

= 10 \cdot \int x x d x

Simplify

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

f (x) = 3 x - 8

\int \frac{( x ^{2} + x + 1 )}{( x + 1 ) ^{2} ( x + 2 )} d x

y = a csc^{2} (k x)

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