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/(sin^2(x))+1)in(x)

Lösung

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

Lösung

d (ln tan (\frac{x}{2}) - cos (x)) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

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

= d \cdot \int \frac{1}{sin ( x )} + sin (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

= d (\int \frac{1}{sin ( x )} d x + \int sin (x) d x)

\int \frac{1}{sin ( x )} d x = ln tan (\frac{x}{2})

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

= d (ln tan (\frac{x}{2}) - cos (x))

Füge eine Konstante zur Lösung hinzu

= d (ln tan (\frac{x}{2}) - cos (x)) + C

Graph

Beliebte Beispiele

integral of-5/3 x^{-31}

\int - \frac{5}{3} x^{- 31} d x

integral of 3/(xln(7x))

\int \frac{3}{x ln ( 7 x )} d x

integral of 5^{x^4}x^3

\int 5^{x^{4}} x^{3} d x

integral of 5/(sqrt(2x+1))

\int \frac{5}{2 x + 1} d x

integral of xe^{cx}

\int x e^{c x} d x