What is the integral from 1 to 5 of 5x-5/x ?

The integral from 1 to 5 of 5x-5/x is 60-5ln(5)

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integral from 1 to 5 of 5x-5/x

\int_{1}^{5} 5 x - \frac{5}{x} d x

60 - 5 ln (5)

Decimal Notation

51.95281 \dots

Solution steps

\int_{1}^{5} 5 x - \frac{5}{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_{1}^{5} 5 x d x - \int_{1}^{5} \frac{5}{x} d x

\int_{1}^{5} 5 x d x = 60

\int_{1}^{5} \frac{5}{x} d x = 5 ln (5)

= 60 - 5 ln (5)

\int \frac{x ^{5}}{( 2 - x ^{6} ) ^{2}} d x

\frac{\partial}{\partial x} (2 y - 1)

n \to \infty lim (\frac{( cos ( \frac{1}{n} ) - 1 )}{\frac{1}{n}})

\int - 5 t d t

\frac{d}{d x} (\frac{1 - 2 x}{3 + x})

What is the integral from 1 to 5 of 5x-5/x ?
The integral from 1 to 5 of 5x-5/x is 60-5ln(5)