What is the integral of (x^3)/(sqrt(5-x^4)) ?

The integral of (x^3)/(sqrt(5-x^4)) is -1/2 sqrt(5-x^4)+C

Popular >

integral of (x^3)/(sqrt(5-x^4))

\int \frac{x ^{3}}{5 - x ^{4}} d x

- \frac{1}{2} 5 - x^{4} + C

Solution steps

\int \frac{x ^{3}}{5 - x ^{4}} d x

Apply u-substitution

: \int - \frac{1}{4 u} d u

= \int - \frac{1}{4 u} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= - \frac{1}{4} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 5 - x^{4}

= - \frac{1}{4} \cdot 2 (5 - x^{4})^{\frac{1}{2}}

Simplify

- \frac{1}{4} \cdot 2 (5 - x^{4})^{\frac{1}{2}} : - \frac{1}{2} 5 - x^{4}

= - \frac{1}{2} 5 - x^{4}

Add a constant to the solution

= - \frac{1}{2} 5 - x^{4} + C

\int \frac{ln ( 1 + x )}{1 + x} d x

\int \frac{2}{( x - 6 ) ( x - 4 )} d x

\int r^{2} e^{- \frac{2 r}{a}} d r

\int 9 \cdot x^{- 6} - 81 \cdot x^{- 8} d x

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

What is the integral of (x^3)/(sqrt(5-x^4)) ?
The integral of (x^3)/(sqrt(5-x^4)) is -1/2 sqrt(5-x^4)+C