What is the integral of (14x^2)/(x^4-25x^2+144) ?

The integral of (14x^2)/(x^4-25x^2+144) is 3ln|x+3|-3ln|x-3|-4ln|x+4|+4ln|x-4|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (14x^2)/(x^4-25x^2+144)

\int \frac{14 x ^{2}}{x ^{4} - 25 x ^{2} + 144} d x

3 ln ∣ x + 3 ∣ - 3 ln ∣ x - 3 ∣ - 4 ln ∣ x + 4 ∣ + 4 ln ∣ x - 4 ∣ + C

Solution steps

\int \frac{14 x ^{2}}{x ^{4} - 25 x ^{2} + 144} d x

Take the constant out:

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

= 14 \cdot \int \frac{x ^{2}}{x ^{4} - 25 x ^{2} + 144} d x

Take the partial fraction of

\frac{x ^{2}}{x ^{4} - 25 x ^{2} + 144} : \frac{3}{14 ( x + 3 )} - \frac{3}{14 ( x - 3 )} - \frac{2}{7 ( x + 4 )} + \frac{2}{7 ( x - 4 )}

= 14 \cdot \int \frac{3}{14 ( x + 3 )} - \frac{3}{14 ( x - 3 )} - \frac{2}{7 ( x + 4 )} + \frac{2}{7 ( x - 4 )} d x

Apply the Sum Rule:

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

= 14 (\int \frac{3}{14 ( x + 3 )} d x - \int \frac{3}{14 ( x - 3 )} d x - \int \frac{2}{7 ( x + 4 )} d x + \int \frac{2}{7 ( x - 4 )} d x)

\int \frac{3}{14 ( x + 3 )} d x = \frac{3}{14} ln ∣ x + 3 ∣

\int \frac{3}{14 ( x - 3 )} d x = \frac{3}{14} ln ∣ x - 3 ∣

\int \frac{2}{7 ( x + 4 )} d x = \frac{2}{7} ln ∣ x + 4 ∣

\int \frac{2}{7 ( x - 4 )} d x = \frac{2}{7} ln ∣ x - 4 ∣

= 14 (\frac{3}{14} ln ∣ x + 3 ∣ - \frac{3}{14} ln ∣ x - 3 ∣ - \frac{2}{7} ln ∣ x + 4 ∣ + \frac{2}{7} ln ∣ x - 4 ∣)

Simplify

14 (\frac{3}{14} ln ∣ x + 3 ∣ - \frac{3}{14} ln ∣ x - 3 ∣ - \frac{2}{7} ln ∣ x + 4 ∣ + \frac{2}{7} ln ∣ x - 4 ∣) : 3 ln ∣ x + 3 ∣ - 3 ln ∣ x - 3 ∣ - 4 ln ∣ x + 4 ∣ + 4 ln ∣ x - 4 ∣

= 3 ln ∣ x + 3 ∣ - 3 ln ∣ x - 3 ∣ - 4 ln ∣ x + 4 ∣ + 4 ln ∣ x - 4 ∣

Add a constant to the solution

= 3 ln ∣ x + 3 ∣ - 3 ln ∣ x - 3 ∣ - 4 ln ∣ x + 4 ∣ + 4 ln ∣ x - 4 ∣ + C

\int \frac{sin ^{3} ( y )}{1 + cos ( y )} d y

\int \frac{cot ^{2} ( t )}{csc ( t )} d t

\int \frac{x ^{2} - 4}{x ^{2} - 16} d x

\int \frac{1}{x ^{0.99}} d x

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

What is the integral of (14x^2)/(x^4-25x^2+144) ?
The integral of (14x^2)/(x^4-25x^2+144) is 3ln|x+3|-3ln|x-3|-4ln|x+4|+4ln|x-4|+C