What is the integral from 1 to 9 of (sqrt(x)-1/x) ?

The integral from 1 to 9 of (sqrt(x)-1/x) is 52/3-2ln(3)

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integral from 1 to 9 of (sqrt(x)-1/x)

\int_{1}^{9} (x - \frac{1}{x}) d x

\frac{52}{3} - 2 ln (3)

Decimal

15.13610 \dots

Solution steps

\int_{1}^{9} x - \frac{1}{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}^{9} x d x - \int_{1}^{9} \frac{1}{x} d x

\int_{1}^{9} x d x = \frac{52}{3}

\int_{1}^{9} \frac{1}{x} d x = 2 ln (3)

= \frac{52}{3} - 2 ln (3)

\int_{- 1}^{5} (x^{\frac{1}{3}} - x) d x

\int_{0}^{1} x^{2} 2^{x^{3}} d x

\int_{1}^{e} ln (x^{3}) d x

\int_{- 4}^{4} - ∣ x ∣ + 4 d x

\int_{3}^{5} (2 x + 9) d x

What is the integral from 1 to 9 of (sqrt(x)-1/x) ?
The integral from 1 to 9 of (sqrt(x)-1/x) is 52/3-2ln(3)