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

The integral of (x^4)/(3+x^5) is 1/5 ln|3+x^5|+C

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

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

\frac{1}{5} ln 3 + x^{5} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = 3 + x^{5}

= \frac{1}{5} ln 3 + x^{5}

Add a constant to the solution

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

\int \frac{x ^{3} + 5 x ^{2} - x + 4}{x} d x

\int \frac{x ^{3}}{( x ^{4} - 5 ) ^{7}} d x

\int 2 x + 2 x d x

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

\int cos (2 x) tan (x) d x

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