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Beliebt Rechnen >

integral of (sin(3t+10))/(cos^2(3t+10))

Lösung

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t

Lösung

\frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10) + C

Schritte zur Lösung

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t

Wende die partielle Integration an

= sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - \int - 10 cos (3 t + 10) + sin (10 + 3 t) d t

\int - 10 cos (3 t + 10) + sin (10 + 3 t) d t = - \frac{10}{3} sin (3 t + 10) - \frac{1}{3} cos (10 + 3 t)

= sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - (- \frac{10}{3} sin (3 t + 10) - \frac{1}{3} cos (10 + 3 t))

Vereinfache

sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - (- \frac{10}{3} sin (3 t + 10) - \frac{1}{3} cos (10 + 3 t)) : \frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10)

= \frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10) + C

Graph

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