integral of sec(t)[tan(t)+sec(t)]

Lösung

\int sec (t) [tan (t) + sec (t)] d t

sec (t) + tan (t) + C

Schritte zur Lösung

\int sec (t) [tan (t) + sec (t)] d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{sin ( t ) + 1}{cos ^{2} ( t )} d t

Multipliziere aus

\frac{sin ( t ) + 1}{cos ^{2} ( t )} : \frac{sin ( t )}{cos ^{2} ( t )} + \frac{1}{cos ^{2} ( t )}

= \int \frac{sin ( t )}{cos ^{2} ( t )} + \frac{1}{cos ^{2} ( t )} d t

Wende die Summenregel an:

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

= \int \frac{sin ( t )}{cos ^{2} ( t )} d t + \int \frac{1}{cos ^{2} ( t )} d t

\int \frac{sin ( t )}{cos ^{2} ( t )} d t = sec (t)

\int \frac{1}{cos ^{2} ( t )} d t = tan (t)

= sec (t) + tan (t)

Füge eine Konstante zur Lösung hinzu

= sec (t) + tan (t) + C

\int \frac{1}{4 x - 3 a} d x

\int (8 x + 9) 4 x^{2} + 9 x d x

\int 7 x^{8} d x

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

\int \frac{x}{x + a} d x