What is the integral from 2 to 3 of (x^3-1/x) ?

The integral from 2 to 3 of (x^3-1/x) is 65/4-ln(3)+ln(2)

Popular >

integral from 2 to 3 of (x^3-1/x)

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

\frac{65}{4} - ln (3) + ln (2)

Decimal

15.84453 \dots

Solution steps

\int_{2}^{3} x^{3} - \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_{2}^{3} x^{3} d x - \int_{2}^{3} \frac{1}{x} d x

\int_{2}^{3} x^{3} d x = \frac{65}{4}

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

= \frac{65}{4} - (ln (3) - ln (2))

Simplify

= \frac{65}{4} - ln (3) + ln (2)

\int_{π}^{l n (x)} cos (e^{t}) d t

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

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

\int_{1}^{6} \frac{1}{x ^{2} + 2 x} d x

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

What is the integral from 2 to 3 of (x^3-1/x) ?
The integral from 2 to 3 of (x^3-1/x) is 65/4-ln(3)+ln(2)