integral of x/((1-x^2)^{1/2)}

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

x^{4} + y^{3} x^{5} + 4 y^{^{'}} = 0

n = 1 \sum \infty \frac{2}{3 ^{n - 1}}

\int 5 cot^{4} (x) d x

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\frac{d}{d t} (f (t))