integral of (6x+1)sqrt(2x-3)

Lösung

\int (6 x + 1) 2 x - 3 d x

\frac{6}{5} x (2 x - 3)^{\frac{3}{2}} + \frac{23}{15} (2 x - 3)^{\frac{3}{2}} + C

Schritte zur Lösung

\int (6 x + 1) 2 x - 3 d x

Multipliziere aus

(6 x + 1) 2 x - 3 : 6 x 2 x - 3 + 2 x - 3

= \int 6 x 2 x - 3 + 2 x - 3 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 6 x 2 x - 3 d x + \int 2 x - 3 d x

\int 6 x 2 x - 3 d x = \frac{6}{5} (x + 1) (2 x - 3)^{\frac{3}{2}}

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

= \frac{6}{5} (x + 1) (2 x - 3)^{\frac{3}{2}} + \frac{1}{3} (2 x - 3)^{\frac{3}{2}}

Vereinfache

\frac{6}{5} (x + 1) (2 x - 3)^{\frac{3}{2}} + \frac{1}{3} (2 x - 3)^{\frac{3}{2}} : \frac{6}{5} x (2 x - 3)^{\frac{3}{2}} + \frac{23}{15} (2 x - 3)^{\frac{3}{2}}

= \frac{6}{5} x (2 x - 3)^{\frac{3}{2}} + \frac{23}{15} (2 x - 3)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{6}{5} x (2 x - 3)^{\frac{3}{2}} + \frac{23}{15} (2 x - 3)^{\frac{3}{2}} + C

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

f (x) = 4 x^{2} sin (4 x)

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

\int_{0}^{1} e^{- 2 x} d x

a re a y = x, x = 4