What is the integral of (3x^2)/(1+x^3) ?

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

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integral of (3x^2)/(1+x^3)

\int \frac{3 x ^{2}}{1 + x ^{3}} d x

ln 1 + x^{3} + C

Solution steps

\int \frac{3 x ^{2}}{1 + x ^{3}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x ^{2}}{1 + x ^{3}} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

= 3 \cdot \int \frac{1}{3 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{3} ln ∣ u ∣

Substitute back

u = 1 + x^{3}

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

Simplify

3 \cdot \frac{1}{3} ln 1 + x^{3} : ln 1 + x^{3}

= ln 1 + x^{3}

Add a constant to the solution

= ln 1 + x^{3} + C

\frac{\partial}{\partial x} (16 - x^{2} - 4 y)

x \to \infty lim (\frac{2}{x !})

\frac{( csc ^{2} ( x ) )}{4}, 4 sin^{2} (x)

\frac{d ^{4}}{d x ^{4}} (cos (x))

\int v d v

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