What is the integral from 1 to e of (24+ln(x))^2 ?

The integral from 1 to e of (24+ln(x))^2 is 577e-530

Popular >

integral from 1 to e of (24+ln(x))^2

\int_{1}^{e} (24 + ln (x))^{2} d x

577 e - 530

Decimal Notation

1038.44861 \dots

Solution steps

\int_{1}^{e} (24 + ln (x))^{2} d x

24 + ln (x) = 24 (1 + \frac{ln ( x )}{24})

= \int_{1}^{e} (24 (1 + \frac{ln ( x )}{24}))^{2} d x

Simplify

(24 (1 + \frac{ln ( x )}{24}))^{2} : 576 + 48 ln (x) + ln^{2} (x)

= \int_{1}^{e} 576 + 48 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} 576 d x + \int_{1}^{e} 48 ln (x) d x + \int_{1}^{e} ln^{2} (x) d x

\int_{1}^{e} 576 d x = 576 e - 576

\int_{1}^{e} 48 ln (x) d x = 48

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

= 576 e - 576 + 48 + e - 2

Simplify

= 577 e - 530

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

\int_{0}^{1} e^{x} e^{x} + 4 d x

\int_{0}^{2 π} 2 - 2 cos (x) d x

\int_{0}^{\frac{1}{2}} 4 e^{2 x} d x

\int_{- 1}^{0} x (x^{2} - 1)^{10} d x

What is the integral from 1 to e of (24+ln(x))^2 ?
The integral from 1 to e of (24+ln(x))^2 is 577e-530