integral of sqrt(x)(1+x)

Lösung

\int x (1 + x) d x

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

Schritte zur Lösung

\int x (1 + x) d x

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int sin^{2} (4 x) cos^{5} (4 x) d x

\int \frac{( x ^{3} )}{4} d x

\int \frac{e ^{3 x}}{e ^{3 x} - 1} d x

\int 10 x^{5} d x

\int sin (6 x) sin (x) d x