What is the integral of (x^3)/(x^2-100) ?

The integral of (x^3)/(x^2-100) is 1/2 (x^2-100+100ln|x^2-100|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^3)/(x^2-100)

\int \frac{x ^{3}}{x ^{2} - 100} d x

\frac{1}{2} (x^{2} - 100 + 100 ln x^{2} - 100) + C

Solution steps

\int \frac{x ^{3}}{x ^{2} - 100} d x

Apply u-substitution

: \int \frac{u + 100}{2 u} d u

= \int \frac{u + 100}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{u + 100}{u} d u

Expand

\frac{u + 100}{u} : 1 + \frac{100}{u}

= \frac{1}{2} \cdot \int 1 + \frac{100}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d u + \int \frac{100}{u} d u)

\int 1 d u = u

\int \frac{100}{u} d u = 100 ln ∣ u ∣

= \frac{1}{2} (u + 100 ln ∣ u ∣)

Substitute back

u = x^{2} - 100

= \frac{1}{2} (x^{2} - 100 + 100 ln x^{2} - 100)

Add a constant to the solution

= \frac{1}{2} (x^{2} - 100 + 100 ln x^{2} - 100) + C

n = 1 \sum \infty \frac{2}{n ^{2} + 4 n + 2}

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

\frac{d}{d x} ((x^{2} - 4)^{2} (x - 1))

\frac{( 1 - 5 t )}{2 + t}

\frac{\partial}{\partial x} (\frac{1}{2 π t} e^{- \frac{( x - y ) ^{2}}{2 t}})

What is the integral of (x^3)/(x^2-100) ?
The integral of (x^3)/(x^2-100) is 1/2 (x^2-100+100ln|x^2-100|)+C