integral of sec^2(x)+sec(2x)tan(2x)

Lösung

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

tan (x) + \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x) + C

Schritte zur Lösung

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

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

\int sec (2 x) tan (2 x) d x = \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)

= tan (x) + \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)

Füge eine Konstante zur Lösung hinzu

= tan (x) + \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x) + C

d er i v a t i v e p (θ) = 7 θ

f (x) = ln (x + 4)

\int \frac{1}{2 sin ( x ) - 3 cos ( x ) - 5} d x

x \to \infty lim (\frac{0}{0})

in v erse l a pl a ce \frac{s + 3}{( s + 1 ) ^{2}}