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

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

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

\int \frac{( x ^{3} )}{( x ^{4} + 5 )} d x

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

Solution steps

\int \frac{x ^{3}}{x ^{4} + 5} 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 = x^{4} + 5

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{6}{sec ( 2 x ) - 1} d x

\int (a - b y)^{4} d y

x \to 5 + lim (x^{2} + 2 x - 3)

\frac{\partial}{\partial y} (sin (2 y + x) sin (x))

n = 0 \sum \infty 3 n - 1

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