erweitern ((ln(6x+1))/(x+2)+(6ln(3x+6))/(6x+1))(3x+6)^{ln(6x+1)}

Lösung

erweitern

(\frac{ln ( 6 x + 1 )}{x + 2} + \frac{6 ln ( 3 x + 6 )}{6 x + 1}) (3 x + 6)^{l n (6 x + 1)}

\frac{ln ( 6 x + 1 ) ( 3 x + 6 ) ^{l n (6 x + 1)}}{x + 2} + \frac{6 ln ( 3 x + 6 ) ( 3 x + 6 ) ^{l n (6 x + 1)}}{6 x + 1}

Schritte zur Lösung

(\frac{ln ( 6 x + 1 )}{x + 2} + \frac{6 ln ( 3 x + 6 )}{6 x + 1}) (3 x + 6)^{l n (6 x + 1)}

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (3 x + 6)^{l n (6 x + 1)}, b = \frac{ln ( 6 x + 1 )}{x + 2}, c = \frac{6 ln ( 3 x + 6 )}{6 x + 1}

= (3 x + 6)^{l n (6 x + 1)} \frac{ln ( 6 x + 1 )}{x + 2} + (3 x + 6)^{l n (6 x + 1)} \frac{6 ln ( 3 x + 6 )}{6 x + 1}

= \frac{ln ( 6 x + 1 )}{x + 2} (3 x + 6)^{l n (6 x + 1)} + \frac{6 ln ( 3 x + 6 )}{6 x + 1} (3 x + 6)^{l n (6 x + 1)}

Vereinfache

\frac{ln ( 6 x + 1 )}{x + 2} (3 x + 6)^{l n (6 x + 1)} + \frac{6 ln ( 3 x + 6 )}{6 x + 1} (3 x + 6)^{l n (6 x + 1)} : \frac{ln ( 6 x + 1 ) ( 3 x + 6 ) ^{l n (6 x + 1)}}{x + 2} + \frac{6 ln ( 3 x + 6 ) ( 3 x + 6 ) ^{l n (6 x + 1)}}{6 x + 1}

= \frac{ln ( 6 x + 1 ) ( 3 x + 6 ) ^{l n (6 x + 1)}}{x + 2} + \frac{6 ln ( 3 x + 6 ) ( 3 x + 6 ) ^{l n (6 x + 1)}}{6 x + 1}

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

e x p an d \frac{z ^{4} - 3 z + 6}{( z + 1 ) ^{3}}

s im pl i f y \frac{( 1 - i ) ^{7}}{( 1 + i ) ^{9}}

s im pl i f y \frac{4 ( 3 x ^{\frac{2}{3}} 3 x - 2 ( x + 1 ) )}{9 3 x x ^{\frac{4}{3}}}

e x p an d \frac{26}{( x - 1 ) ( x + 1 )}