What is the integral from 1 to 4 of 1+1/u+1/(u^2) ?

The integral from 1 to 4 of 1+1/u+1/(u^2) is 2ln(2)+15/4

Popular >

integral from 1 to 4 of 1+1/u+1/(u^2)

\int_{1}^{4} 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

2 ln (2) + \frac{15}{4}

Decimal

5.13629 \dots

Solution steps

\int_{1}^{4} 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}^{4} 1 d u + \int_{1}^{4} \frac{1}{u} d u + \int_{1}^{4} \frac{1}{u ^{2}} d u

\int_{1}^{4} 1 d u = 3

\int_{1}^{4} \frac{1}{u} d u = 2 ln (2)

\int_{1}^{4} \frac{1}{u ^{2}} d u = \frac{3}{4}

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

Combine the fractions

3 + \frac{3}{4} : \frac{15}{4}

= 2 ln (2) + \frac{15}{4}

\int_{x}^{x^{3}} e^{t^{2}} d t

\int_{0}^{2} 4 - y^{2} d y

\int_{0}^{1} 3^{5 x} d x

\int_{0}^{6} (3 x^{2} + 1) d x

\int_{1}^{32} x^{- \frac{4}{5}} d x

What is the integral from 1 to 4 of 1+1/u+1/(u^2) ?
The integral from 1 to 4 of 1+1/u+1/(u^2) is 2ln(2)+15/4