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Beliebt Rechnen >

integral of ((6x^3+6x))/(x^2+1)

Lösung

\int \frac{( 6 x ^{3} + 6 x )}{x ^{2} + 1} d x

Lösung

3 x^{2} + 3 + C

Schritte zur Lösung

\int \frac{6 x ^{3} + 6 x}{x ^{2} + 1} d x

Multipliziere aus

\frac{6 x ^{3} + 6 x}{x ^{2} + 1} : \frac{6 x ^{3}}{x ^{2} + 1} + \frac{6 x}{x ^{2} + 1}

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{6 x ^{3}}{x ^{2} + 1} d x + \int \frac{6 x}{x ^{2} + 1} d x

\int \frac{6 x ^{3}}{x ^{2} + 1} d x = 3 (x^{2} + 1 - ln x^{2} + 1)

\int \frac{6 x}{x ^{2} + 1} d x = 3 ln x^{2} + 1

= 3 (x^{2} + 1 - ln x^{2} + 1) + 3 ln x^{2} + 1

Vereinfache

3 (x^{2} + 1 - ln x^{2} + 1) + 3 ln x^{2} + 1 : 3 x^{2} + 3

= 3 x^{2} + 3

Füge eine Konstante zur Lösung hinzu

= 3 x^{2} + 3 + C

Graph

Beliebte Beispiele

\frac{d y}{d x} + 3 y = 6

integral of e^{-x}(x-1)

\int e^{- x} (x - 1) d x

derivative of (x+2/(10-3x))

\frac{d}{d x} (\frac{x + 2}{10 - 3 x})

implicit (dy)/(dx),ax^3-3b^2xy+cy(x)^3=1

im pl i c i t \frac{d y}{d x}, a x^{3} - 3 b^{2} x y + cy (x)^{3} = 1

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

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