de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summenregel an:

\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}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of (3+5x-8sqrt(x)/x)

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

derivative f(x)=cos(a^3+x^3)

d er i v a t i v e f (x) = cos (a^{3} + x^{3})

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

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

integral of 6xsqrt(x+2)

\int 6 x x + 2 d x

integral of 8sqrt(x/4+1)

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