de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/(cos^2(x)sqrt(1+tan^2(x)))

Lösung

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

Lösung

ln ∣ tan (x) + sec (x) ∣ + C

Schritte zur Lösung

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

Vereinfache

\frac{1}{cos ^{2} ( x ) 1 + tan ^{2} ( x )} : sec^{2} (x)

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

sec^{2} (x) = (sec (x)),

angenommen

sec (x) \geq 0

= \int sec (x) d x

Nutze das gemeinsame Integral :

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= ln ∣ tan (x) + sec (x) ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ tan (x) + sec (x) ∣ + C

Graph

Beliebte Beispiele

integral of x^{16}

\int x^{16} d x

integral of cos(3-2x)

\int cos (3 - 2 x) d x

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

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

integral of 1/((2-x)^3)

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

integral of-xsin(xy)

\int - x sin (x y) d y