What is the integral from 1 to 4 of 1/(sqrt(1+x^2)) ?

The integral from 1 to 4 of 1/(sqrt(1+x^2)) is ln(sqrt(17)+4)-ln(sqrt(2)+1)

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integral from 1 to 4 of 1/(sqrt(1+x^2))

\int_{1}^{4} \frac{1}{1 + x ^{2}} d x

ln (17 + 4) - ln (2 + 1)

Decimal

1.21333 \dots

Solution steps

\int_{1}^{4} \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]_{1}^{4}

Compute the boundaries:

ln (17 + 4) - ln (2 + 1)

= ln (17 + 4) - ln (2 + 1)

\int_{0}^{x} t^{2} + 4 d t

\int_{x^{2}}^{x^{4}} sin (t) d t

\int_{0}^{1 - y^{2}} x y^{2} d x

\int_{1}^{4} 2 x - 3 d x

\int_{2}^{6} 4 x d x

What is the integral from 1 to 4 of 1/(sqrt(1+x^2)) ?
The integral from 1 to 4 of 1/(sqrt(1+x^2)) is ln(sqrt(17)+4)-ln(sqrt(2)+1)