展开 30(1/3 sin(3x)-1/2 cos(2x)+1/5 e^{5x}+C)

解答

展开

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

10 sin (3 x) - 15 cos (2 x) + 6 e^{5 x} + 30 C

求解步骤

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

打开括号

= 30 \cdot \frac{1}{3} sin (3 x) + 30 (- \frac{1}{2} cos (2 x)) + 30 \cdot \frac{1}{5} e^{5 x} + 30 C

使用加减运算法则

+ (- a) = - a

= 30 \cdot \frac{1}{3} sin (3 x) - 30 \cdot \frac{1}{2} cos (2 x) + 30 \cdot \frac{1}{5} e^{5 x} + 30 C

化简

30 \cdot \frac{1}{3} sin (3 x) - 30 \cdot \frac{1}{2} cos (2 x) + 30 \cdot \frac{1}{5} e^{5 x} + 30 C : 10 sin (3 x) - 15 cos (2 x) + 6 e^{5 x} + 30 C

= 10 sin (3 x) - 15 cos (2 x) + 6 e^{5 x} + 30 C

e x p an d (6 x y^{2} + 2 y) d x + (3 x^{2} y + 6 y^{2}) d y

e x p an d \frac{2 k}{( ( 2 j w + 1 ) ( j w + 1 ) ( j w + 2 ) )}

e x p an d \frac{6 x ^{2}}{( x - 1 ) ^{4}}

e x p an d \frac{( x - 1 ) ( 3 x ^{2} + 3 x + 2 )}{( x + 1 )}

e x p an d \frac{x ^{3} - 4 x ^{2} + 5 x + 1}{x ( x - 1 ) ^{2}}