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Beliebt Rechnen >

integral of 1/(1-sin(5x))

Lösung

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

Lösung

\frac{1}{5} tan (5 x) + \frac{1}{5} sec (5 x) + C

Schritte zur Lösung

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

Multipliziere mit der Konjugation von

1 - sin (5 x) : \frac{cos ^{2} ( 5 x )}{1 + sin ( 5 x )}

= \int \frac{1}{\frac{c o s ^{2} ( 5 x )}{1 + s i n ( 5 x )}} d x

Multipliziere aus

\frac{1}{\frac{c o s ^{2} ( 5 x )}{1 + s i n ( 5 x )}} : \frac{1}{cos ^{2} ( 5 x )} + \frac{sin ( 5 x )}{cos ^{2} ( 5 x )}

= \int \frac{1}{cos ^{2} ( 5 x )} + \frac{sin ( 5 x )}{cos ^{2} ( 5 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 \frac{1}{cos ^{2} ( 5 x )} d x + \int \frac{sin ( 5 x )}{cos ^{2} ( 5 x )} d x

\int \frac{1}{cos ^{2} ( 5 x )} d x = \frac{1}{5} tan (5 x)

\int \frac{sin ( 5 x )}{cos ^{2} ( 5 x )} d x = \frac{1}{5} sec (5 x)

= \frac{1}{5} tan (5 x) + \frac{1}{5} sec (5 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} tan (5 x) + \frac{1}{5} sec (5 x) + C

Graph

Beliebte Beispiele

derivative of 16xsin(x)

\frac{d}{d x} (16 x sin (x))

integral of 1/((5x+3)^2)

\int \frac{1}{( 5 x + 3 ) ^{2}} d x

integral from 0 to 1 of (x-sqrt(x))/3

\int_{0}^{1} \frac{x - x}{3} d x

integral of e^{ax}cos(x)

\int e^{a x} cos (x) d x

integral of (x^2+2)/(x^3+6x)

\int \frac{x ^{2} + 2}{x ^{3} + 6 x} d x