What is the integral of (1+y^2)/(1+x^2) ?

The integral of (1+y^2)/(1+x^2) is (1+y^2)arctan(x)+C

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integral of (1+y^2)/(1+x^2)

\int \frac{1 + y ^{2}}{1 + x ^{2}} d x

(1 + y^{2}) arctan (x) + C

Solution steps

\int \frac{1 + y ^{2}}{1 + x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (1 + y^{2}) \cdot \int \frac{1}{1 + x ^{2}} d x

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

= (1 + y^{2}) arctan (x)

Add a constant to the solution

= (1 + y^{2}) arctan (x) + C

\frac{d}{d x} (x e^{- x} - e^{- x})

n = 1 \sum \infty n 3^{- n}

x \to 0 lim (\frac{1}{3 x})

x y^{^{'}} - y = x ln (x)

4^{x} x^{4}

What is the integral of (1+y^2)/(1+x^2) ?
The integral of (1+y^2)/(1+x^2) is (1+y^2)arctan(x)+C