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Popular Calculus >

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

Solution

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

Solution

\frac{5}{2}

+1

Decimal

2.5

Solution steps

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

Expand

x (1 + \frac{1}{x}) : x + 1

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

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

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

= \frac{3}{2} + 1

Simplify

\frac{3}{2} + 1 : \frac{5}{2}

= \frac{5}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of x(1+1/x) ?
The integral from 1 to 2 of x(1+1/x) is 5/2