What is the integral from 0 to 3 of ln(x^2+1) ?

The integral from 0 to 3 of ln(x^2+1) is 3ln(10)-2(-arctan(3)+3)

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integral from 0 to 3 of ln(x^2+1)

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

3 ln (10) - 2 (- arctan (3) + 3)

Decimal Notation

3.40584 \dots

Solution steps

\int_{0}^{3} 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]_{0}^{3}

= [x ln (x^{2} + 1) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{0}^{3}

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

= [x ln (x^{2} + 1) - 2 (- arctan (x) + x)]_{0}^{3}

Compute the boundaries:

3 ln (10) - 2 (- arctan (3) + 3)

= 3 ln (10) - 2 (- arctan (3) + 3)

t \to 1 lim (\frac{sin ( 3 t ) - 3}{t})

x \to \infty lim ((9)^{x})

f (t) = 4 t^{2} cos (2 t) + 5 t e^{- 7 t}

\frac{1}{9 x ^{2}}

(x^{3} + 2 x + 7) (2 + \frac{1}{x ^{2}})

What is the integral from 0 to 3 of ln(x^2+1) ?
The integral from 0 to 3 of ln(x^2+1) is 3ln(10)-2(-arctan(3)+3)