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- 7. Use substitution to evaluate 2x(4 – x2) dx.Find the indefinite integral and check the result by differentiation. dx 5 - 9x2 Part 1 of 7 (5 - x²). g(x) = (5 – 9x²). Observe that is the derivative of Let Multiply and divide the integrand by and rewrite the integral. 1 -3 5 - 9x2) dx = 9x2) (-18x) dxUse the Substitution Rule to prove that∫sin2ax dx =(x/2) -(sin(2ax)/4a )+ C
- Evaluate the indefinite x² – 9x 32 -dx (x – 3)(x + 2)?Find the indefinite integral and check the result by differentiation. dx 9x2 Part 1 of 7 Observe that-18x is the derivative of (5 - 9x?). Let g(x) = (5 – 9x2). %3D -18x Multiply and divide the integrand by -18 -18 and rewrite the integral. 1 -3 9x2 dx = - 18 / (5 - 9x²)°(-18x) dx 18 Part 2 of 7 (s - 2²) * -3 | -3 9x2 Now, g'(x) = Define f(g(x)) : such that f(x) = %3D -18 -18 Rewrite the given integral in terms of g(x). 1 -3 dx = 9x2 (-18x) dx 5 - 5 – 9x2 - Ja f( (x))g'(x) dx %D »] + c F(g( f(g(x))g'(x) dx = F(g(x)) + C %3D where F(g(x)) is the antiderivative of f(g(x)).Evaluate x(x2 + 1)3 dx.