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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{x ^{2}}{( y ^{2} + x ^{2} ) ^{\frac{1}{2}}} - \int \frac{y ^{2} x}{( y ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{y ^{2} x}{( y ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x = - \frac{y ^{2}}{( y ^{2} + x ^{2} ) ^{\frac{1}{2}}}

= \frac{x ^{2}}{( y ^{2} + x ^{2} ) ^{\frac{1}{2}}} - (- \frac{y ^{2}}{( y ^{2} + x ^{2} ) ^{\frac{1}{2}}})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x^2+2yz

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

integral of 1/(2sqrt(x-x^2))

\int \frac{1}{2 x - x ^{2}} d x

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\int \frac{15 x ^{2} - 4 x - 28}{x ^{3} - 4 x} d x

integral of 7xsqrt(x^2+5)

\int 7 x x^{2} + 5 d x

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