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Beliebt Rechnen >

integral of sec(t)(4sec(t)+7tan(t))

Lösung

\int sec (t) (4 sec (t) + 7 tan (t)) d t

Lösung

4 tan (t) + 7 sec (t) + C

Schritte zur Lösung

\int sec (t) (4 sec (t) + 7 tan (t)) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{4 + 7 sin ( t )}{cos ^{2} ( t )} d t

Multipliziere aus

\frac{4 + 7 sin ( t )}{cos ^{2} ( t )} : \frac{4}{cos ^{2} ( t )} + \frac{7 sin ( t )}{cos ^{2} ( t )}

= \int \frac{4}{cos ^{2} ( t )} + \frac{7 sin ( t )}{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{4}{cos ^{2} ( t )} d t + \int \frac{7 sin ( t )}{cos ^{2} ( t )} d t

\int \frac{4}{cos ^{2} ( t )} d t = 4 tan (t)

\int \frac{7 sin ( t )}{cos ^{2} ( t )} d t = 7 sec (t)

= 4 tan (t) + 7 sec (t)

Füge eine Konstante zur Lösung hinzu

= 4 tan (t) + 7 sec (t) + C

Graph

Beliebte Beispiele

\frac{d}{d y} (y e^{x})

limit as x approaches-infinity of x^{-2}

x \to - \infty lim (x^{- 2})

x^2y^{''}+7xy^'+8y=0,y(1)=0,y^'(1)=-5

x^{2} y^{^{''}} + 7 x y^{^{'}} + 8 y = 0, y (1) = 0, y^{^{'}} (1) = - 5

derivative of (x^3/2+1/(6x))

\frac{d}{d x} (\frac{x ^{3}}{2} + \frac{1}{6 x})

integral of xsqrt(2x^2-1)

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