integral of ((8+5x)/(1+x^2))

Lösung

\int (\frac{8 + 5 x}{1 + x ^{2}}) d x

8 arctan (x) + \frac{5}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{8 + 5 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{8 + 5 x}{1 + x ^{2}} : \frac{8}{1 + x ^{2}} + \frac{5 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{8}{1 + x ^{2}} d x + \int \frac{5 x}{1 + x ^{2}} d x

\int \frac{8}{1 + x ^{2}} d x = 8 arctan (x)

\int \frac{5 x}{1 + x ^{2}} d x = \frac{5}{2} ln 1 + x^{2}

= 8 arctan (x) + \frac{5}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 8 arctan (x) + \frac{5}{2} ln 1 + x^{2} + C

\frac{d}{d x} (4 x^{4} + x^{3} - \frac{9 x ^{2}}{2} + 8 x)

t a y l or sin (π x), \frac{1}{2}

(cos^{2} (t))^{^{'}}

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