What is the integral of 10xsqrt(x) ?

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

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integral of 10xsqrt(x)

\int 10 x 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

\int \frac{- 1 ( x - 9 )}{( x + 5 ) ( x - 2 )} d x

y^{^{'}} + x y = - x^{3}

\frac{d ^{2}}{d x ^{2}} (x^{5} e^{x})

y = 7 x

x \to - \infty lim (3^{x})