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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{6}{5} x^{\frac{5}{2}} + \frac{3 x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}} - x + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 3 x^{\frac{3}{2}} d x = \frac{6}{5} x^{\frac{5}{2}}

\int 3 x d x = \frac{3 x ^{2}}{2}

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

= \frac{6}{5} x^{\frac{5}{2}} + \frac{3 x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}} - x + C

Graph

Beliebte Beispiele

integral of (sin(3x))/(sqrt(2+cos(3x)))

\int \frac{sin ( 3 x )}{2 + cos ( 3 x )} d x

integral of arcos(x)

\int a r cos (x) d x

derivative y=xsqrt((a^2-x^2)/x)

d er i v a t i v e y = x \frac{a ^{2} - x ^{2}}{x}

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a re a x = y^{2} - 12, x = 4 y

integral of cos(y)e^{5sin(y)}

\int cos (y) e^{5 s i n (y)} d y