Final answer:
To evaluate the given integral, we can use the integration by parts method by setting u = x and dv = 5sin³(x) dx. Simplifying the steps using the formula for integration by parts, the integral becomes -x*cos(x) + sin(x) + C, where C is the constant of integration.
Step-by-step explanation:
To evaluate the integral ∫(5sin³(x) * x) dx, we can use the integration by parts method. Let u = x and dv = 5sin³(x) dx. Taking the derivatives and antiderivatives, we have du = dx and v = -cos(x). Using the formula for integration by parts, ∫udv = uv - ∫vdu, we can evaluate the integral:
∫(5sin³(x) * x) dx = -x*cos(x) - ∫(-cos(x) dx)
Simplifying further, the integral becomes -x*cos(x) + sin(x) + C, where C is the constant of integration.