integrate cos^2(2x)sin^3(2x) dx
To integrate this we need to use the chain rule, substituting cos2x = u Integral becomes: u2sin32x dxChain rule: dy/dx = du/dx dy/du du/dx = -2sin2x --> dx = -1/2sin2x du Substituting into the equation u2sin32x * -1/2sin2x du Simplifies to: -2u2sin22x duWe know that cos2x + sin2x =1 Integral = -2u2(1 - cos22x) du Substituting -> -2u2 + 2u4 duIntegrating this: -2( 1/3u3 - 1/5u5) + c Substituting u back into the equation: cos52x/10 - cos32x/6 + c
LW
Related Maths A Level answers
All answers ▸How do you show that two lines do, or do not intersect?
Show that the determinant of the 3x3 matrix (2 1 1 / 2 1 7 / 6 3 5) is equal to zero.
If x is a real number, what are the solutions to the quadratic: 4*x^2- 4*x+1 = 0
Find the range of a degree-2 polynomial function such as 2x^2 +1, or x^2 + 2x - 3.