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

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_{1}^{4} f (x + 6) d x

\int_{- 1}^{0} \frac{x ^{2} + 4 x - 1}{x + 2} d x

\int_{1}^{2} \frac{ln ( 2 x )}{x} d x

\int_{0}^{2} ln (x + 4) d x

\int_{0}^{1} x 3 x + 1 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)