What is the integral from 1 to 6 of x/2+1/(2x) ?

The integral from 1 to 6 of x/2+1/(2x) is 35/4+1/2 ln(6)

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integral from 1 to 6 of x/2+1/(2x)

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

\frac{35}{4} + \frac{1}{2} ln (6)

Decimal Notation

9.64587 \dots

Solution steps

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

\int_{1}^{6} \frac{x}{2} d x = \frac{35}{4}

\int_{1}^{6} \frac{1}{2 x} d x = \frac{1}{2} ln (6)

= \frac{35}{4} + \frac{1}{2} ln (6)

\int e^{- \frac{1}{2 x}} d x

m (x) = x^{3} - x^{2} + 1

x \to 10.6 lim (ln (x^{2} - 9))

\int x^{- 3} + x^{\frac{1}{4}} d x

\int sin^{\frac{1}{2}} (x) d x

What is the integral from 1 to 6 of x/2+1/(2x) ?
The integral from 1 to 6 of x/2+1/(2x) is 35/4+1/2 ln(6)