What is the integral from 1 to e of (14+ln(x))^2 ?

The integral from 1 to e of (14+ln(x))^2 is 197e-170

Popular >

integral from 1 to e of (14+ln(x))^2

\int_{1}^{e} (14 + ln (x))^{2} d x

197 e - 170

Decimal Notation

365.50152 \dots

Solution steps

\int_{1}^{e} (14 + ln (x))^{2} d x

Expand

(14 + ln (x))^{2} : 196 + 28 ln (x) + ln^{2} (x)

= \int_{1}^{e} 196 + 28 ln (x) + ln^{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}^{e} 196 d x + \int_{1}^{e} 28 ln (x) d x + \int_{1}^{e} ln^{2} (x) d x

\int_{1}^{e} 196 d x = 196 e - 196

\int_{1}^{e} 28 ln (x) d x = 28

\int_{1}^{e} ln^{2} (x) d x = e - 2

= 196 e - 196 + 28 + e - 2

Simplify

= 197 e - 170

\int_{- 1}^{0} (x e^{y} - y) d x

\int_{1}^{5} \frac{5}{2} e^{0.4 x} d x

\int_{0}^{r} (b r^{3} + c r^{2}) d r

\int_{1}^{5} (\frac{3 x}{x ^{3}}) d x

\int_{0}^{a} sin (x) d x

What is the integral from 1 to e of (14+ln(x))^2 ?
The integral from 1 to e of (14+ln(x))^2 is 197e-170