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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply u-substitution

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

= \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = x^{3} + 1

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

Add a constant to the solution

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

Popular Examples

(dy}{dx}=\frac{(-xe^{-x^2}))/y

\frac{d y}{d x} = \frac{( - x e ^{- x^{2}} )}{y}

integral of 8x^2cos(2x)

\int 8 x^{2} cos (2 x) d x

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

\int (x^{2} + 1)^{3} \cdot x d x

sum from n=1 to infinity of (1/n)(1/n)^2

n = 1 \sum \infty (\frac{1}{n}) (\frac{1}{n})^{2}

y^'=(2xy)/(x^2+1)

y^{^{'}} = \frac{2 x y}{x ^{2} + 1}

Frequently Asked Questions (FAQ)

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