What is the substitution integral of (((x^3))/((x^4-5))),u=x^4-5 ?

The substitution integral of (((x^3))/((x^4-5))),u=x^4-5 is 1/4 ln|x^4-5|+C

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Integrate Using u-Substitution integral of (x^3)/(x^4-5) with respect to x , u=x^4-5

substitution

\int (\frac{( x ^{3} )}{( x ^{4} - 5 )}) d x, u = x^{4} - 5

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

Solution steps

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

Apply u-substitution:

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

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

x \to 1 - lim (\frac{( x - 1 )}{( x ^{2} - 4 )})

(- 3, 3), (5, 9)

x \to - \infty lim (\frac{( x ^{4} - 1 )}{( x ^{3} - 1 )})

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

\int (\frac{( x ^{2} - 9 )}{( x ^{3} )}) d x

What is the substitution integral of (((x^3))/((x^4-5))),u=x^4-5 ?
The substitution integral of (((x^3))/((x^4-5))),u=x^4-5 is 1/4 ln|x^4-5|+C