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

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

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integral of y/(x^2+1)

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

y arctan (x) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= y arctan (x)

Add a constant to the solution

= y arctan (x) + C

\frac{d}{d x} (2000 - 4 x)

\int \frac{1}{16 x ^{2} + 9} d x

(x^{2} + x y) d x - x^{2} d y = 0

\frac{d}{d x} (- x cos (x) + cos (x))

y = x^{4} + 8 x^{2} - x