Question

谁的导数是cosθ的4次方？

Answer 1

(cosx)^4的原函数求解过程为：

∫(cosx)^4dx

=∫[(1+cos2x)/2]^2dx

=1/4∫[1+2cos2x+(cos2x)^2]dx

=1/4∫dx+1/4∫2cos2xdx+1/4∫(cos2x)^2dx

=x/4+C+1/4∫cos2xd(2x)+1/4∫[(1+cos4x)/2]dx

=x/4+(sin2x)/4+C+1/4∫1/2dx+1/4∫(cos4x)/2dx

=3x/8+(sin2x)/4+C+1/32∫4cos4xdx

=3x/8+(sin2x)/4+C+1/32∫cos4xd(4x)

=3x/8+(sin2x)/4+(sin4x)/32+C

Answer 2

cos^2θ=(cos2+θ1)/2 cos^4θ=(cos^2)θ^2=[(cos2+θ1)/2]^2=(cos^22+θ2cos2θ+1)/4=[(cos4+θ1)/2+2cos2θ+1]/4=cos4θ/8+cos2/θ2+3/8
∫cos4θ/8+cos2θ/2+3/8 d θ=sin4θ/32+sin2θ/4+3θ/8+C sin4θ/32+sin2θ/4+3θ/8+C 的导数是 cos^4θ

Answer 3

对这个函数积分就知道了

Answer 4

追答

求采纳(=^_^=)

Answer 5

1*sin^5/5