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

Lösung

erweitern

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

x^{2} ln (x + 2) d x - x^{2} d x

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = x^{2} d x, b = ln (x + 2), c = 1

= x^{2} d x ln (x + 2) - x^{2} d x \cdot 1

= x^{2} ln (x + 2) d x - 1 \cdot x^{2} d x

Multipliziere:

1 \cdot x^{2} = x^{2}

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

e x p an d \frac{4}{x ( x + 2 )}

s im pl i f y (x - 8 - 5) (x - 8 + 5)

e x p an d (1 - sec (x))^{2}

e x p an d \frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{2} + 1 ) ^{2}}

e x p an d \frac{s ^{2} + 7}{( s - 2 ) ^{2} ( s ^{2} + 10 s + 50 )}