use the given trig identity to set up a u substitution and then evaluate the indefinite integral ∫cos^39xdx, c?
use the given trig identity to set up a u substitution and then evaluate the indefinite integral
∫cos^3(9x)dx, cos^2(9x)=1-sin^2(9x)
please explain how to solve this problem :)
More Questions From This User See All
Answers & Comments
Verified answer
cos(9x)^3 * dx =>
cos(9x)^2 * cos(9x) * dx =>
(1 - sin(9x)^2) * cos(9x) * dx =>
cos(9x) * dx - sin(9x)^2 * cos(9x) * dx
u = sin(9x)
du = 9 * cos(9x) * dx
du / 9 = cos(9x) * dx
(1/9) * du - (1/9) * u^2 * du
Integrate
(1/9) * u - (1/9) * (1/3) * u^3 + C =>
(1/27) * u * (3 - u^2) + C =>
(1/27) * sin(9x) * (3 - sin(9x)^2) + C
With the given identity the problem becomes [1-sin^2(9x)]cos(9x)dx, sub u = sin(9x) so du = 9cos(9x), and the problem becomes (1/9)[1-u^2]du, then solve
i think of you will desire to permit u = e^3x. Then du/dx = 3e^3x = 3u so dx = a million/(3u) du ?3e^(3x)sin(e^3x) dx = ?3u sin u . a million/(3u) du = ? sin u du = -cos u + C = -cos (e^3x) + C i think of the 2nd question will choose a trigonometric substitution, yet i'm uncertain what it quite is going to likely be on the 2nd.