What is the integral of ((5x^2))/(sqrt(1-5x^3)) ?

The integral of ((5x^2))/(sqrt(1-5x^3)) is -2/3 sqrt(1-5x^3)+C

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integral of ((5x^2))/(sqrt(1-5x^3))

\int \frac{( 5 x ^{2} )}{1 - 5 x ^{3}} d x

- \frac{2}{3} 1 - 5 x^{3} + C

Solution steps

\int \frac{5 x ^{2}}{1 - 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 \frac{x ^{2}}{1 - 5 x ^{3}} d x

Apply u-substitution

: \int - \frac{1}{15 u} d u

= 5 \cdot \int - \frac{1}{15 u} d u

Take the constant out:

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

= 5 (- \frac{1}{15} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 5 (- \frac{1}{15} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 1 - 5 x^{3}

= 5 (- \frac{1}{15} \cdot 2 (1 - 5 x^{3})^{\frac{1}{2}})

Simplify

5 (- \frac{1}{15} \cdot 2 (1 - 5 x^{3})^{\frac{1}{2}}) : - \frac{2}{3} 1 - 5 x^{3}

= - \frac{2}{3} 1 - 5 x^{3}

Add a constant to the solution

= - \frac{2}{3} 1 - 5 x^{3} + C

x \to 0 + lim (sin (\frac{π}{x}))

\frac{\partial}{\partial x} (y - x^{2})

2 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{(- y)}

\int \frac{2}{3} t^{\frac{3}{2}} - 2 sin (t) + C d t

\int (5 x - x^{2}) d x

What is the integral of ((5x^2))/(sqrt(1-5x^3)) ?
The integral of ((5x^2))/(sqrt(1-5x^3)) is -2/3 sqrt(1-5x^3)+C