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

The integral from 0 to 5 of 1/(1+x^2+y^2) is 5/(x^2+y^2+1)

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

\int_{0}^{5} \frac{1}{1 + x ^{2} + y ^{2}} d z

\frac{5}{x ^{2} + y ^{2} + 1}

Solution steps

\int_{0}^{5} \frac{1}{1 + x ^{2} + y ^{2}} d z

Integral of a constant:

\int a d x = a x

= [\frac{1}{1 + x ^{2} + y ^{2}} z]_{0}^{5}

Multiply

\frac{1}{1 + x ^{2} + y ^{2}} z : \frac{z}{1 + x ^{2} + y ^{2}}

= [\frac{z}{1 + x ^{2} + y ^{2}}]_{0}^{5}

Compute the boundaries:

\frac{5}{x ^{2} + y ^{2} + 1}

= \frac{5}{x ^{2} + y ^{2} + 1}

\int_{y}^{2 y} 8 x + e^{y} d x

\int_{- 1}^{3} 6 x^{5} - 2 x^{3} + 2 d x

\int_{2}^{4} - x^{3} + 6 x^{2} - 8 x d x

\int_{0}^{1} tan (π) x d x

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