de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{2} ln 1 + x^{2} + \frac{arctan ^{2} ( x )}{2} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{x}{1 + x ^{2}} d x = \frac{1}{2} ln 1 + x^{2}

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

= \frac{1}{2} ln 1 + x^{2} + \frac{arctan ^{2} ( x )}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln 1 + x^{2} + \frac{arctan ^{2} ( x )}{2} + C

Graph

Beliebte Beispiele

derivative of x^{arcsin(x})

\frac{d}{d x} (x^{a r c s i n (x)})

derivative of (4x+4sqrt(1+x)/(x^2-1))

\frac{d}{d x} (\frac{4 x + 4 1 + x}{x ^{2} - 1})

integral of (8x^2+10)/(x^3+5x)

\int \frac{8 x ^{2} + 10}{x ^{3} + 5 x} d x

x^3=(2sqrt(y^5+4))/(5y^4y^')

x^{3} = \frac{2 y ^{5} + 4}{5 y ^{4} y ^{^{'}}}

integral of sin(16x)cos(7x)

\int sin (16 x) cos (7 x) d x