integral of (x^2)/((x^2-36)^{5/2)}

Lösung

\int \frac{x ^{2}}{( x ^{2} - 36 ) ^{\frac{5}{2}}} d x

\frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}} + C

Schritte zur Lösung

\int \frac{x ^{2}}{( x ^{2} - 36 ) ^{\frac{5}{2}}} d x

Wende die partielle Integration an

= \frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \int - \frac{5 x ^{4}}{3 ( x ^{2} - 36 ) ^{\frac{7}{2}}} d x

\int - \frac{5 x ^{4}}{3 ( x ^{2} - 36 ) ^{\frac{7}{2}}} d x = \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}}

= \frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}} + C

\frac{d}{d x} (x^{5} tan (x))

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