erweitern (x^2-x+2)dx(x+1)(x+2)(x-3)

Lösung

erweitern

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

x^{5} d x - x^{4} d x - 5 x^{3} d x + x^{2} d x - 8 x d x - 12 d x

Schritte zur Lösung

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

Multipliziere aus

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

= d x (x^{3} + x + 2) (x + 2) (x - 3)

Multipliziere aus

(x^{3} + x + 2) (x + 2) : x^{4} + 2 x^{3} + x^{2} + 4 x + 4

= d x (x^{4} + 2 x^{3} + x^{2} + 4 x + 4) (x - 3)

Multipliziere aus

(x^{4} + 2 x^{3} + x^{2} + 4 x + 4) (x - 3) : x^{5} - x^{4} - 5 x^{3} + x^{2} - 8 x - 12

= d x (x^{5} - x^{4} - 5 x^{3} + x^{2} - 8 x - 12)

Multipliziere aus

d x (x^{5} - x^{4} - 5 x^{3} + x^{2} - 8 x - 12) : x^{5} d x - x^{4} d x - 5 x^{3} d x + x^{2} d x - 8 x d x - 12 d x

= x^{5} d x - x^{4} d x - 5 x^{3} d x + x^{2} d x - 8 x d x - 12 d x

e x p an d x I n g res a (a + b)^{2}

e x p an d \frac{( ln ( x ^{2} + y ^{2} ) + e ^{5 x - z} ) ^{2}}{2}

e x p an d \frac{\partial}{\partial x} ((100 - 5 x) \cdot x) - 20 x

e x p an d 30 e^{6 (\frac{t}{8} - 2)} sin (4) (\frac{t}{8} - 2) H (\frac{t}{8} - 2)

e x p an d 12 x + 3 (2 x - 4 = 60)