What is the integral from-2 to 2 of (1/((x+4)(x-4))) ?

The integral from-2 to 2 of (1/((x+4)(x-4))) is -1/4 ln(3)

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integral from-2 to 2 of (1/((x+4)(x-4)))

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

- \frac{1}{4} ln (3)

Decimal Notation

- 0.27465 \dots

Solution steps

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

Take the partial fraction of

\frac{1}{( x + 4 ) ( x - 4 )} : - \frac{1}{8 ( x + 4 )} + \frac{1}{8 ( x - 4 )}

= \int_{- 2}^{2} - \frac{1}{8 ( x + 4 )} + \frac{1}{8 ( 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

= - \int_{- 2}^{2} \frac{1}{8 ( x + 4 )} d x + \int_{- 2}^{2} \frac{1}{8 ( x - 4 )} d x

\int_{- 2}^{2} \frac{1}{8 ( x + 4 )} d x = \frac{1}{8} ln (3)

\int_{- 2}^{2} \frac{1}{8 ( x - 4 )} d x = - \frac{1}{8} ln (3)

= - \frac{1}{8} ln (3) - \frac{1}{8} ln (3)

Simplify

- \frac{1}{8} ln (3) - \frac{1}{8} ln (3) : - \frac{1}{4} ln (3)

= - \frac{1}{4} ln (3)

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What is the integral from-2 to 2 of (1/((x+4)(x-4))) ?
The integral from-2 to 2 of (1/((x+4)(x-4))) is -1/4 ln(3)