What is the integral of (x^2)/((x^3+14)^2) ?

The integral of (x^2)/((x^3+14)^2) is -1/(3(x^3+14))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2)/((x^3+14)^2)

\int \frac{x ^{2}}{( x ^{3} + 14 ) ^{2}} d x

- \frac{1}{3 ( x ^{3} + 14 )} + C

Solution steps

\int \frac{x ^{2}}{( x ^{3} + 14 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{3 u ^{2}} d u

= \int \frac{1}{3 u ^{2}} 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 ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= \frac{1}{3} (- \frac{1}{u})

Substitute back

u = x^{3} + 14

= \frac{1}{3} (- \frac{1}{x ^{3} + 14})

Simplify

\frac{1}{3} (- \frac{1}{x ^{3} + 14}) : - \frac{1}{3 ( x ^{3} + 14 )}

= - \frac{1}{3 ( x ^{3} + 14 )}

Add a constant to the solution

= - \frac{1}{3 ( x ^{3} + 14 )} + C

\int \frac{4 - e ^{x}}{e ^{9 x}} d x

\int (- \frac{1}{y}) d y

\int (4 x^{2} + 7 + \frac{2}{x ^{2} + 1}) d x

\int 2 x \cdot (x^{2} + 1)^{5} d x

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

What is the integral of (x^2)/((x^3+14)^2) ?
The integral of (x^2)/((x^3+14)^2) is -1/(3(x^3+14))+C