What is the integral from 0 to 1 of ln(x^2+5) ?

The integral from 0 to 1 of ln(x^2+5) is 2sqrt(5)arctan(1/(sqrt(5)))+ln(6)-2

Popular >

integral from 0 to 1 of ln(x^2+5)

\int_{0}^{1} ln (x^{2} + 5) d x

25 arctan (\frac{1}{5}) + ln (6) - 2

Decimal

1.67244 \dots

Solution steps

\int_{0}^{1} ln (x^{2} + 5) d x

Apply Integration By Parts

: [x ln (x^{2} + 5) - \int \frac{2 x ^{2}}{x ^{2} + 5} d x]_{0}^{1}

= [x ln (x^{2} + 5) - \int \frac{2 x ^{2}}{x ^{2} + 5} d x]_{0}^{1}

\int \frac{2 x ^{2}}{x ^{2} + 5} d x = - 25 arctan (\frac{x}{5}) + 2 x

= [x ln (x^{2} + 5) - (- 25 arctan (\frac{x}{5}) + 2 x)]_{0}^{1}

Simplify

= [x ln (x^{2} + 5) + 25 arctan (\frac{x}{5}) - 2 x]_{0}^{1}

Compute the boundaries:

25 arctan (\frac{1}{5}) + ln (6) - 2

= 25 arctan (\frac{1}{5}) + ln (6) - 2

\int_{- 8}^{4} (- 2 x + 8) d x

\int_{0}^{3} (x^{2} - 9) d x

\int_{0}^{6} - 6 x^{2} - 18 x + 324 d x

\int_{- π}^{0} (π + x) \cdot cos (n x) d x

\int_{- 4}^{- 2} \frac{9}{x ^{2}} d x

What is the integral from 0 to 1 of ln(x^2+5) ?
The integral from 0 to 1 of ln(x^2+5) is 2sqrt(5)arctan(1/(sqrt(5)))+ln(6)-2