integral of (2+7x)/(1+x^2)

Lösung

\int \frac{2 + 7 x}{1 + x ^{2}} d x

2 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{2 + 7 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{2 + 7 x}{1 + x ^{2}} : \frac{2}{1 + x ^{2}} + \frac{7 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{2}{1 + x ^{2}} d x + \int \frac{7 x}{1 + x ^{2}} d x

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

\int \frac{7 x}{1 + x ^{2}} d x = \frac{7}{2} ln 1 + x^{2}

= 2 arctan (x) + \frac{7}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 2 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

\int e^{x} 4 - e^{x} d x

a re a 6 - x, x, 1

\frac{d}{d x} (\frac{8 x}{7 - cot ( x )})

a re a x ln (x), - x + 1, [1, 3]

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