展开 f(x^2-x+2)sin(3x)dx

解答

展开

f (x^{2} - x + 2) sin (3 x) d x

f x^{2} sin (3 x) d x - f x sin (3 x) d x + 2 f sin (3 x) d x

求解步骤

f (x^{2} - x + 2) sin (3 x) d x

= f sin (3 x) (x^{2} - x + 2) d x

打开括号

= f sin (3 x) d x x^{2} + f sin (3 x) d x (- x) + f sin (3 x) d x \cdot 2

使用加减运算法则

+ (- a) = - a

= f x^{2} sin (3 x) d x - f x sin (3 x) d x + 2 f sin (3 x) d x

e x p an d \frac{( x + 10 )}{( x - 1 ) ^{2}}

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

e x p an d (3 x + 7) e^{x}

e x p an d ln (ln (x^{3} (x + 1)))

e x p an d b^{2} (4 b^{2} - 2 b = 2)