What is the integral of (x^3)/((2+x^4)) ?

The integral of (x^3)/((2+x^4)) is 1/4 ln|2+x^4|+C

Popular >

integral of (x^3)/((2+x^4))

\int \frac{x ^{3}}{( 2 + x ^{4} )} d x

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

Solution steps

\int \frac{x ^{3}}{2 + 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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} ln ∣ u ∣

Substitute back

u = 2 + x^{4}

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

Add a constant to the solution

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

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

\int \frac{1}{x ( x + 4 x + 5 )} d x

\int sin^{3} (5 x + 1) d x

\int x e^{- 15 x} d x

\int \frac{2 x - 7}{6 x ^{2} - 5 x + 1} d x

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