Find the antiderivative of the following function using the method of integratio

Question

Find the antiderivative of the following function using the method of integration by substitution. h(t) = 24 sin(3t) / (10-2 cos(3t))5 / 2 Recall that integration by substitution relies on the "reverse" of the Chain rule of derivatives. This can be written, h(t)dt = f(g(t))g'(t)dt = f(u)du where u = g(t) is the substitution. What substitution will you make? U = g(t) = Enter just an expression in t. What is the function f(u) in the new integral f(u) du ? f(u) = Enter just an expression in u, do not include a du and do not integrate yet! Be very careful of the constants. What is the indefinite integral of the function f(u) in the new variable u? f(u) du = Enter just an expression in u, and do not forget the constant of integration! What is the indefinite integral of the function F(t) in the variable t? f(g(t)) g'(t) dt = Just back substitute using your answers to parts 1 and 3.

Explanation / Answer

put c0s3t = y -3 sin3t dt = dy -8dy/(10 - 2y)^(5/2) now you can integrate its east after integration out value of y back

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