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

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

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integral from 0 to 1 of 1/(sqrt(1+x^2))

\int_{0}^{1} \frac{1}{1 + x ^{2}} d x

ln (1 + 2)

Decimal

0.88137 \dots

Solution steps

\int_{0}^{1} \frac{1}{1 + x ^{2}} d x

Use the common integral:

\int \frac{1}{1 + x ^{2}} d x = ln x^{2} + 1 + x

= [ln x^{2} + 1 + x]_{0}^{1}

Compute the boundaries:

ln (1 + 2)

= ln (1 + 2)

\int e^{1 - 3 x} d x

y^{^{''}} + 2 y = e x + x^{3}

x \to 9 + lim (\frac{1}{x - 9})

t an g e n t y = x^{4}, (- 1, 1)

d er i v a t i v e 5 t + 6 t^{5}

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