erweitern ((1-sin(x)+t^2)t)/((1+t^2)^2)

Lösung

erweitern

\frac{( 1 - sin ( x ) + t ^{2} ) t}{( 1 + t ^{2} ) ^{2}}

\frac{t - t sin ( x ) + t ^{3}}{1 + 2 t ^{2} + t ^{4}}

Schritte zur Lösung

\frac{( 1 - sin ( x ) + t ^{2} ) t}{( 1 + t ^{2} ) ^{2}}

(1 + t^{2})^{2} = 1 + 2 t^{2} + t^{4}

= \frac{t ( t ^{2} + 1 - sin ( x ) )}{1 + 2 t ^{2} + t ^{4}}

Multipliziere aus

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

= \frac{t - t sin ( x ) + t ^{3}}{1 + 2 t ^{2} + t ^{4}}

e x p an d (2 cos (x) - 1) (2 cos (x) + 1)

e x p an d 4 (x + h) - 3 - 4 x - 3

e x p an d x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

\frac{d}{d x} (x^{4} - 2 x^{3} - 4 x^{2} - 5 x + 2)

s im pl i f y \frac{1}{2} (- \frac{1}{7} cos (7 x) + cos (x)) + C