What is the integral from 4 to 12 of (x-4/x) ?

The integral from 4 to 12 of (x-4/x) is 64-4ln(3)

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integral from 4 to 12 of (x-4/x)

\int_{4}^{12} (x - \frac{4}{x}) d x

64 - 4 ln (3)

Decimal Notation

59.60555 \dots

Solution steps

\int_{4}^{12} x - \frac{4}{x} 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_{4}^{12} x d x - \int_{4}^{12} \frac{4}{x} d x

\int_{4}^{12} x d x = 64

\int_{4}^{12} \frac{4}{x} d x = 4 ln (3)

= 64 - 4 ln (3)

\int_{- \frac{π}{2}}^{- \frac{π}{3}} sec^{2} (3 x) d x

\int_{0}^{x} 3 x d x

\int_{0}^{x} x sin (y) d y

\int_{- 1}^{3} 9 - x^{2} d x

What is the integral from 4 to 12 of (x-4/x) ?
The integral from 4 to 12 of (x-4/x) is 64-4ln(3)