求积分 ∫2x^3+(1/x^2)-sinx dx1.∫ 2x^3+(1/x^2)-sinx dx2.∫ (cosx -sinx)_数学解答

求积分 ∫2x^3+(1/x^2)-sinx dx
1.∫ 2x^3+(1/x^2)-sinx dx
2.∫ (cosx -sinx)^2 dx
3..∫ x ln x^2 dx
4.∫ d (sinx- 2x^2)

人气：205 ℃　时间：2020-05-09 15:39:43

解答

1) ∫ 2x^3 + 1/x^2 - sinx dx = 2/4*x^4 - 1/x + cosx + C = 1/2*x^4 - 1/x + cosx + C
2) ∫ (cosx - sinx)^2 dx = ∫ cos^2x - 2sinxcosx + sin^2x dx = ∫ 1 - sin2x dx = x + 1/2*cos2x + C
3) ∫ xlnx^2 dx = ∫ 2lnx dx^2/2 = x^2*lnx - ∫ x^2 dlnx = x^2*lnx - ∫ x^2*1/x dx = x^2*lnx - ∫ x dx
= x^2*lnx - x^2/2 + C
4) ∫ d(sinx - 2x^2) = sinx - 2x^2 + C