erweitern sec(x/2)tan(x/2)+2(x-10)^3+e^{5x}

Lösung

erweitern

sec (\frac{x}{2}) tan (\frac{x}{2}) + 2 (x - 10)^{3} + e^{5 x}

sec (\frac{x}{2}) tan (\frac{x}{2}) + 2 x^{3} - 60 x^{2} + 600 x - 2000 + e^{5 x}

Schritte zur Lösung

sec (\frac{x}{2}) tan (\frac{x}{2}) + 2 (x - 10)^{3} + e^{5 x}

(x - 10)^{3} = x^{3} - 30 x^{2} + 300 x - 1000

= sec (\frac{x}{2}) tan (\frac{x}{2}) + 2 (x^{3} - 30 x^{2} + 300 x - 1000) + e^{5 x}

Multipliziere aus

2 (x^{3} - 30 x^{2} + 300 x - 1000) : 2 x^{3} - 60 x^{2} + 600 x - 2000

= sec (\frac{x}{2}) tan (\frac{x}{2}) + 2 x^{3} - 60 x^{2} + 600 x - 2000 + e^{5 x}

s im pl i f y (3 + 5 i)^{5}

e x p an d 3 (b x - c)^{2} + 3 (b x - c) + 1

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

e x p an d \frac{323 x ^{6}}{( 2 x ^{7} + 4 ) ^{3}}

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