What is the integral from 1 to 5 of (1+1/u+1/(u^2)) ?

The integral from 1 to 5 of (1+1/u+1/(u^2)) is ln(5)+24/5

Popular >

integral from 1 to 5 of (1+1/u+1/(u^2))

\int_{1}^{5} (1 + \frac{1}{u} + \frac{1}{u ^{2}}) d u

ln (5) + \frac{24}{5}

Decimal

6.40943 \dots

Solution steps

\int_{1}^{5} 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

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}^{5} 1 d u + \int_{1}^{5} \frac{1}{u} d u + \int_{1}^{5} \frac{1}{u ^{2}} d u

\int_{1}^{5} 1 d u = 4

\int_{1}^{5} \frac{1}{u} d u = ln (5)

\int_{1}^{5} \frac{1}{u ^{2}} d u = \frac{4}{5}

= 4 + ln (5) + \frac{4}{5}

Combine the fractions

4 + \frac{4}{5} : \frac{24}{5}

= ln (5) + \frac{24}{5}

\int_{6}^{5} sin (x) d x

\int_{x}^{x^{2}} e^{x^{7}} d x

\int_{1}^{2} e^{x - 1} d x

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

\int_{0}^{3} (32 x^{3} + 4 x) d x

What is the integral from 1 to 5 of (1+1/u+1/(u^2)) ?
The integral from 1 to 5 of (1+1/u+1/(u^2)) is ln(5)+24/5