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Beliebt Rechnen >

integral of (2x+3)(sqrt(2x-1))

Lösung

\int (2 x + 3) (2 x - 1) d x

Lösung

\frac{2}{5} x (2 x - 1)^{\frac{3}{2}} + \frac{17}{15} (2 x - 1)^{\frac{3}{2}} + C

Schritte zur Lösung

\int (2 x + 3) 2 x - 1 d x

Multipliziere aus

(2 x + 3) 2 x - 1 : 2 x 2 x - 1 + 3 2 x - 1

= \int 2 x 2 x - 1 + 3 2 x - 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x 2 x - 1 d x + \int 3 2 x - 1 d x

\int 2 x 2 x - 1 d x = \frac{2}{15} (3 x + 1) (2 x - 1)^{\frac{3}{2}}

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

= \frac{2}{15} (3 x + 1) (2 x - 1)^{\frac{3}{2}} + (2 x - 1)^{\frac{3}{2}}

Vereinfache

\frac{2}{15} (3 x + 1) (2 x - 1)^{\frac{3}{2}} + (2 x - 1)^{\frac{3}{2}} : \frac{2}{5} x (2 x - 1)^{\frac{3}{2}} + \frac{17}{15} (2 x - 1)^{\frac{3}{2}}

= \frac{2}{5} x (2 x - 1)^{\frac{3}{2}} + \frac{17}{15} (2 x - 1)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x (2 x - 1)^{\frac{3}{2}} + \frac{17}{15} (2 x - 1)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

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

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

integral of-sin^2(2x)

\int - sin^{2} (2 x) d x

integral of x^5e^{-x^4}

\int x^{5} e^{- x^{4}} d x

integral of (sec^2(arctan(2x)))/(1+4x^2)

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

integral of 2x^3+5x^2-3x+1

\int 2 x^{3} + 5 x^{2} - 3 x + 1 d x