What is the integral of 5sqrt(x^3) ?

The integral of 5sqrt(x^3) is 2x^{5/2}+C

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integral of 5sqrt(x^3)

\int 5 x^{3} d x

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

Solution steps

\int 5 x^{3} d x

Take the constant out:

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

= 5 \cdot \int x^{3} d x

x^{3} = x^{\frac{3}{2}},

assuming

x \geq 0

= 5 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\int 2 sec^{2} (x) tan^{3} (x) d x

f^{^{'}} (x) = 2 + 5 x^{2}

\int_{0}^{15} 25 - \frac{8 x}{15} d x

y = x^{2} - 5 x - 2, (3, - 8)

\int \frac{4 x ^{3} + 3 x ^{2} + 2 x + 1}{x ^{2}} d x