展开 3sec(pi/4 (x+1))

解答

展开

3 sec (\frac{π}{4} (x + 1))

\frac{3 2}{cos ( \frac{π x}{4} ) - sin ( \frac{π x}{4} )}

求解步骤

3 sec (\frac{π}{4} (x + 1))

乘开

\frac{π}{4} (x + 1) : \frac{π}{4} x + 1 \cdot \frac{π}{4}

= 3 sec (\frac{π}{4} x + 1 \cdot \frac{π}{4})

使用三角恒等式改写

= 3 \cdot \frac{2}{cos ( \frac{π x}{4} ) - sin ( \frac{π x}{4} )}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 \cdot 3}{cos ( \frac{π x}{4} ) - sin ( \frac{π x}{4} )}

e x p an d ln (cos^{2} (t) + 1) \cdot ((e^{x^{2}} \cdot 2 x) i + sinh (t) j)

e x p an d e^{2 x} (x^{3} + 5)

e x p an d \frac{4 x + 6}{x ( x + 2 )}

e x p an d 2 t (45 cos (3 t) + 16 e^{- 4 t} - 8 sin (2 t))

e x p an d 30 (\frac{1}{3} sin (3 x) - \frac{1}{2} cos (2 x) + \frac{1}{5} e^{5 x} + C)