What is the integral from 1 to 2 of ln|x^2+1| ?

The integral from 1 to 2 of ln|x^2+1| is 2ln(5)+2arctan(2)-2-pi/2-ln(2)

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integral from 1 to 2 of ln|x^2+1|

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

2 ln (5) + 2 arctan (2) - 2 - \frac{π}{2} - ln (2)

Decimal Notation

1.16922 \dots

Solution steps

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

Eliminate Absolutes

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

Apply Integration By Parts

: [x ln (x^{2} + 1) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{1}^{2}

= [x ln (x^{2} + 1) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{1}^{2}

\int \frac{2 x ^{2}}{x ^{2} + 1} d x = 2 (- arctan (x) + x)

= [x ln (x^{2} + 1) - 2 (- arctan (x) + x)]_{1}^{2}

Compute the boundaries:

2 ln (5) + 2 arctan (2) - 2 - \frac{π}{2} - ln (2)

= 2 ln (5) + 2 arctan (2) - 2 - \frac{π}{2} - ln (2)

\frac{d}{d x} (ln (4 x - 1))

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

x y^{^{'}} + 3 y = \frac{4 e ^{2 x}}{x ^{2}}

x \to 1 lim (\frac{2 x}{x - 1})

f (x) = 9 x^{5} (x^{3} - 2 x)

What is the integral from 1 to 2 of ln|x^2+1| ?
The integral from 1 to 2 of ln|x^2+1| is 2ln(5)+2arctan(2)-2-pi/2-ln(2)