de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

sin (x) + tan (x) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{cos ^{3} ( x ) + 1}{cos ^{2} ( x )} : cos (x) + \frac{1}{cos ^{2} ( x )}

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

\int cos (x) d x = sin (x)

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

= sin (x) + tan (x)

Füge eine Konstante zur Lösung hinzu

= sin (x) + tan (x) + C

Graph

Beliebte Beispiele

integral of (x^3)/(9+x^4)

\int \frac{x ^{3}}{9 + x ^{4}} d x

integral of (10)/(x^3+x^2)

\int \frac{10}{x ^{3} + x ^{2}} d x

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

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

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

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

integral of ((3x+2)(x-4))/(x-3)

\int \frac{( 3 x + 2 ) ( x - 4 )}{x - 3} d x