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Beliebt Rechnen >

integral of (7x^6)/(csc(pi+x^7))

Lösung

\int \frac{7 x ^{6}}{csc ( π + x ^{7} )} d x

Lösung

x^{7} sin (π + x^{7}) + x^{7} sin (x^{7}) + cos (x^{7}) + C

Schritte zur Lösung

\int \frac{7 x ^{6}}{csc ( π + x ^{7} )} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int \frac{x ^{6}}{csc ( π + x ^{7} )} d x

Wende die partielle Integration an

= 7 (\frac{1}{7} x^{7} sin (π + x^{7}) - \int - x^{13} cos (x^{7}) d x)

\int - x^{13} cos (x^{7}) d x = - \frac{1}{7} (x^{7} sin (x^{7}) + cos (x^{7}))

= 7 (\frac{1}{7} x^{7} sin (π + x^{7}) - (- \frac{1}{7} (x^{7} sin (x^{7}) + cos (x^{7}))))

Vereinfache

7 (\frac{1}{7} x^{7} sin (π + x^{7}) - (- \frac{1}{7} (x^{7} sin (x^{7}) + cos (x^{7})))) : x^{7} sin (π + x^{7}) + x^{7} sin (x^{7}) + cos (x^{7})

= x^{7} sin (π + x^{7}) + x^{7} sin (x^{7}) + cos (x^{7})

Füge eine Konstante zur Lösung hinzu

= x^{7} sin (π + x^{7}) + x^{7} sin (x^{7}) + cos (x^{7}) + C

Graph

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