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Beliebt Rechnen >

integral of ((4+x))/(1+x^2)

Lösung

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

Lösung

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

Schritte zur Lösung

\int \frac{4 + x}{1 + x ^{2}} d x

Multipliziere aus

\frac{4 + x}{1 + x ^{2}} : \frac{4}{1 + x ^{2}} + \frac{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{4}{1 + x ^{2}} d x + \int \frac{x}{1 + x ^{2}} d x

\int \frac{4}{1 + x ^{2}} d x = 4 arctan (x)

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

= 4 arctan (x) + \frac{1}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 4 arctan (x) + \frac{1}{2} ln 1 + x^{2} + C

Graph

Beliebte Beispiele

integral of (2x^2+4)/(x^3-8)

\int \frac{2 x ^{2} + 4}{x ^{3} - 8} d x

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

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\int \frac{4 x}{( x ^{2} - 1 ) ^{3}} d x

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\int cos (x) cos (4 sin (x)) d x

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\int (3 x + 2)^{10} d x