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Beliebt Rechnen >

integral of 10x(1-x)^5

Lösung

\int 10 x (1 - x)^{5} d x

Lösung

10 (\frac{1}{2} x^{2} (1 - x)^{5} + \frac{1}{42} (35 x^{3} - 105 x^{4} + 126 x^{5} - 70 x^{6} + 15 x^{7})) + C

Schritte zur Lösung

\int 10 x (1 - x)^{5} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int x (1 - x)^{5} d x

Wende die partielle Integration an

= 10 (\frac{1}{2} x^{2} (1 - x)^{5} - \int - \frac{5}{2} x^{2} (1 - x)^{4} d x)

\int - \frac{5}{2} x^{2} (1 - x)^{4} d x = - \frac{1}{42} (35 x^{3} - 105 x^{4} + 126 x^{5} - 70 x^{6} + 15 x^{7})

= 10 (\frac{1}{2} x^{2} (1 - x)^{5} - (- \frac{1}{42} (35 x^{3} - 105 x^{4} + 126 x^{5} - 70 x^{6} + 15 x^{7})))

Vereinfache

= 10 (\frac{1}{2} x^{2} (1 - x)^{5} + \frac{1}{42} (35 x^{3} - 105 x^{4} + 126 x^{5} - 70 x^{6} + 15 x^{7}))

Füge eine Konstante zur Lösung hinzu

= 10 (\frac{1}{2} x^{2} (1 - x)^{5} + \frac{1}{42} (35 x^{3} - 105 x^{4} + 126 x^{5} - 70 x^{6} + 15 x^{7})) + C

Graph

Beliebte Beispiele

integral of x^2(7x^3-3)^5

\int x^{2} (7 x^{3} - 3)^{5} d x

integral of (x^3+2x)(x^4+4x^2+4)^7

\int (x^{3} + 2 x) (x^{4} + 4 x^{2} + 4)^{7} d x

integral of (1-cos(2u))/2

\int \frac{1 - cos ( 2 u )}{2} d u

integral of ((-5x+15))/((x^2+2x+4)^2)

\int \frac{( - 5 x + 15 )}{( x ^{2} + 2 x + 4 ) ^{2}} d x

integral of 1/((x-1)sqrt(x))

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