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

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

Popular >

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

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

\frac{3}{2} + 3 ln (2)

Decimal

3.57944 \dots

Solution steps

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

Expand

\frac{x ^{2} + 3}{x} : x + \frac{3}{x}

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

\int_{1}^{2} x d x = \frac{3}{2}

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

= \frac{3}{2} + 3 ln (2)

\int_{0}^{1} (7 - 8 v^{3} + 16 v^{7}) d v

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

\int_{- 2}^{2} - 2 x^{2} d x

\int_{1}^{e^{5}} \frac{4 ln ( x )}{x} d x

\int_{1}^{6} (\frac{6}{x} - e^{- x}) d x

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