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Beliebt Rechnen >

integral of (2ax+b)/(sqrt(ax^2+bx+c))

Lösung

\int \frac{2 a x + b}{a x ^{2} + b x + c} d x

Lösung

2 a x^{2} + b x + c + C

Schritte zur Lösung

\int \frac{2 a x + b}{a x ^{2} + b x + c} d x

Wende U-Substitution an

= \int \frac{1}{u} d u

Wende die Potenzregel an

= 2 u^{\frac{1}{2}}

Setze in

u = a x^{2} + b x + c

ein

= 2 (a x^{2} + b x + c)^{\frac{1}{2}}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= 2 a x^{2} + b x + c

Füge eine Konstante zur Lösung hinzu

= 2 a x^{2} + b x + c + C

Graph

Beliebte Beispiele

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

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

integral of x/(sqrt(x^2-14x+45))

\int \frac{x}{x ^{2} - 14 x + 45} d x

integral of sqrt(a^2+t^2)

\int a^{2} + t^{2} d t

integral of (tan(x)-sec(x))^2

\int (tan (x) - sec (x))^{2} d x

integral of tan^5(x/(18))

\int tan^{5} (\frac{x}{18}) d x