integral of ((e^{tan(x)}))/(cos^2(x))

Lösung

\int \frac{( e ^{t a n (x)} )}{cos ^{2} ( x )} d x

e^{t a n (x)} + C

Schritte zur Lösung

\int \frac{e ^{t a n (x)}}{cos ^{2} ( x )} d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{e ^{t a n (x)}}{1 - sin ^{2} ( x )} d x

Wende die partielle Integration an

= e^{t a n (x)} tan (x) - \int e^{t a n (x)} sec^{2} (x) tan (x) d x

\int e^{t a n (x)} sec^{2} (x) tan (x) d x = tan (x) e^{t a n (x)} - e^{t a n (x)}

= e^{t a n (x)} tan (x) - (tan (x) e^{t a n (x)} - e^{t a n (x)})

Vereinfache

e^{t a n (x)} tan (x) - (tan (x) e^{t a n (x)} - e^{t a n (x)}) : e^{t a n (x)}

= e^{t a n (x)}

Füge eine Konstante zur Lösung hinzu

= e^{t a n (x)} + C

y^{^{''}} + 5 y^{^{'}} + 2 y = 7

t an g e n t y = 2 x^{3}, (2, 16)

\int \frac{1}{x x + 1} d x

d er i v a t i v e y = (\frac{x}{1 + x})^{5}

\frac{d}{d x} (2 x \cdot e^{x^{2}})