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Beliebt Rechnen >

integral of 7(sec(x))^2-4sin(x)

Lösung

\int 7 (sec (x))^{2} - 4 sin (x) d x

Lösung

7 tan (x) + 4 cos (x) + C

Schritte zur Lösung

\int 7 (sec (x))^{2} - 4 sin (x) d x

Vereinfache

= \int 7 sec^{2} (x) - 4 sin (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 7 sec^{2} (x) d x - \int 4 sin (x) d x

\int 7 sec^{2} (x) d x = 7 tan (x)

\int 4 sin (x) d x = - 4 cos (x)

= 7 tan (x) - (- 4 cos (x))

Vereinfache

= 7 tan (x) + 4 cos (x)

Füge eine Konstante zur Lösung hinzu

= 7 tan (x) + 4 cos (x) + C

Graph

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