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

The integral of (x)/(x^2+y^2) is dy 1/2 ln|y^2+x^2|+C

Popular >

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

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

d y \frac{1}{2} ln y^{2} + x^{2} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= d y \cdot \int \frac{1}{2 u} d u

Take the constant out:

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

= d y \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= d y \frac{1}{2} ln ∣ u ∣

Substitute back

u = y^{2} + x^{2}

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

Add a constant to the solution

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

\int \frac{2 x ^{3} + 4 x ^{2} + 3 x - 1}{x ^{2} + 2 x + 1} d x

\int \frac{6 - 72 x}{49 - 36 x ^{2}} d x

f (x) = (x - 4) (x^{2} + 8), (1, - 27)

x \to 1 - lim (- x^{2} + 5 x + (- 4))

n = 3 \sum \infty \frac{2}{n ln ^{2} ( n )}

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