integral of (sqrt(x)+7)(x-sqrt(x)+1)

Lösung

\int (x + 7) (x - x + 1) d x

\frac{2}{5} x^{\frac{5}{2}} + 3 x^{2} - 4 x^{\frac{3}{2}} + 7 x + C

Schritte zur Lösung

\int (x + 7) (x - x + 1) d x

Multipliziere aus

(x + 7) (x - x + 1) : x^{\frac{3}{2}} + 6 x - 6 x + 7

= \int x^{\frac{3}{2}} + 6 x - 6 x + 7 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^{\frac{3}{2}} d x + \int 6 x d x - \int 6 x d x + \int 7 d x

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

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

\int 6 x d x = 4 x^{\frac{3}{2}}

\int 7 d x = 7 x

= \frac{2}{5} x^{\frac{5}{2}} + 3 x^{2} - 4 x^{\frac{3}{2}} + 7 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x^{\frac{5}{2}} + 3 x^{2} - 4 x^{\frac{3}{2}} + 7 x + C

\int cos^{4} (6 x) sin (6 x) d x

\int sin^{2} (3 u) d u

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

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

\int \frac{3}{1 - cos ( x )} d x