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Beliebt Rechnen >

integral of (4+7x)/(1+x^2)

Lösung

\int \frac{4 + 7 x}{1 + x ^{2}} d x

Lösung

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

Schritte zur Lösung

\int \frac{4 + 7 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{4 + 7 x}{1 + x ^{2}} : \frac{4}{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{4}{1 + x ^{2}} d x + \int \frac{7 x}{1 + x ^{2}} d x

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

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

= 4 arctan (x) + \frac{7}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 4 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

Graph

Beliebte Beispiele

integral from 0 to 1 of 1/(sqrt(16-x^2))

\int_{0}^{1} \frac{1}{16 - x ^{2}} d x

ydx+sqrt(x^2+1)dy=0

y d x + x^{2} + 1 d y = 0

derivative of (5-3x^2)

\frac{d}{d x} ((5 - 3 x)^{2})

integral of 1/((1+x)^{3/4)}

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

sum from n=0 to infinity of (100^n)/(n!)

n = 0 \sum \infty \frac{10 0 ^{n}}{n !}