integral of (1-x^2-3x^2)/(x^{2/3)}

Lösung

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

3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

= 3 x^{\frac{1}{3}} (1 - 4 x^{2}) - \int - 24 x^{\frac{4}{3}} d x

\int - 24 x^{\frac{4}{3}} d x = - \frac{72}{7} x^{\frac{7}{3}}

= 3 x^{\frac{1}{3}} (1 - 4 x^{2}) - (- \frac{72}{7} x^{\frac{7}{3}})

Vereinfache

3 x^{\frac{1}{3}} (1 - 4 x^{2}) - (- \frac{72}{7} x^{\frac{7}{3}}) : 3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}}

= 3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}}

Füge eine Konstante zur Lösung hinzu

= 3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}} + C

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

\int (sec^{2} (x) (1 + tan (x))) d x

\int - e^{- x} sin (e^{- x}) d x

\int x^{\frac{1}{3}} e^{x^{\frac{1}{3}}} d x

\int \frac{4 x ^{3}}{( 1 - 2 x ^{4} ) ^{6}} d x