Question

求下列不定积分或定积分 1,∫（x^4+cosx)dx 2,∫cosxsin^3xdx 3,∫xlnxdx 4,∫|x-

Answer 1

1、 ∫(x^4+cosx) dx = (1/5)x^5+sinx + C 2、 ∫(cosxsin³x) dx = ∫sin³x d(sinx) = (1/4)sin^4x + C 3、 ∫xlnx dx = ∫lnx d(x²/2) = (1/2)x²lnx - (1/2)∫x²*1/x dx = (1/2)x²lnx - (1/2)∫x dx = (1/2)x²lnx - (1/4)x² + C 4、 |x-3|=[√(x-3)]² =-(x-3)=-x+3 for x3,∫(x-3)dx=x²/2-3x + C ∴∫|x-3|dx =x²/2-3x + C for x>3 =-x²/2+3x + C for x