Question

∫ 17 x e¹¹ˣ d x=(A x-B) e¹¹ˣ+ constant, then A/B=__

Answer 1

To evaluate the integral ∫ 17 x e¹¹ˣ d x, we can use integration by parts. The result is (A x - B) e¹¹ˣ + C, with A = 1/11 and B = C.

Step-by-step explanation:

To evaluate the integral ∫ 17 x e¹¹ˣ d x, we can use integration by parts. Let u = x and dv = 17 e¹¹ˣ dx. Taking the derivative of u, we have du = dx, and integrating dv, we get v = (1/11)e¹¹ˣ. Using the integration by parts formula ∫ u dv = uv - ∫ v du, we have: ∫ 17 x e¹¹ˣ d x = (x(1/11)e¹¹ˣ - ∫ (1/11)e¹¹ˣ d x) + C. Integrating ∫ (1/11)e¹¹ˣ d x, we obtain (1/11)e¹¹ˣ, so the final result becomes: ∫ 17 x e¹¹ˣ d x = (A x - B) e¹¹ˣ + C, where A = 1/11 and B = C.