(Solved): Find the indefinite integral and check the result by differentiation. 6x 1 (6-x) dx Step 1 Ob ...

Find the indefinite integral and check the result by differentiation. 6x 1 (6-x²) ³ dx Step 1 Observe that -2x Step 2 Multiply and divide the integrand by - (6-x²) ³? Now, g'(x) = -2x 3 dx = -2x 6x 6x² dx = -3 33³3 is the derivative of (6 – x²). Let g(x) = (6 – x²). - Rewrite the given integral in terms of g(x). and rewrite the integral. =/(@ g - F9CX . Define f(g(x)) = ?3 / (6-x²)-³(-2x) dx f(g(x))g'(x) dx = F(g(x)) + C -3 = -3(6 - x²)-³? such that f(x) = -3 -2x / (6-x²)-3³(-2x) dx (x))g'(x) dx [? ) )] + c fa where F(g(x)) is the antiderivative of f(g(x)). ]x)²