What is the integral from 0 to 0.7 of ln(x^2+1) ?

The integral from 0 to 0.7 of ln(x^2+1) is 0.10059…

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integral from 0 to 0.7 of ln(x^2+1)

\int_{0}^{0.7} ln (x^{2} + 1) d x

0.10059 \dots

Solution steps

\int_{0}^{0.7} 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}^{0.7}

= [x ln (x^{2} + 1) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{0}^{0.7}

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

= [x ln (x^{2} + 1) - 2 (- arctan (x) + x)]_{0}^{0.7}

Compute the boundaries:

0.10059 \dots

= 0.10059 \dots

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What is the integral from 0 to 0.7 of ln(x^2+1) ?
The integral from 0 to 0.7 of ln(x^2+1) is 0.10059…