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

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

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

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

\frac{x}{y} + ln ∣ x ∣ + y^{2} + x^{2} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{y} d x = \frac{x}{y}

\int \frac{1}{x} d x = ln ∣ x ∣

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

= \frac{x}{y} + ln ∣ x ∣ + y^{2} + x^{2}

Add a constant to the solution

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

\frac{d}{d x} (\frac{3 + 5 x - 8 x}{x})

f (x) = cos (a^{3} + x^{3})

y^{^{''}} + 0.5 y^{^{'}} + 4 y = 0

\int 6 x x + 2 d x

\int 8 \frac{x}{4} + 1 d x

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