fk378 said:Why can't my way work?
To find the integral of xcos5x dx, you can use integration by parts method. This involves breaking the integral into two parts and applying the formula: ∫udv = uv - ∫vdu.
When using integration by parts, the general rule is to choose u as the part of the function that becomes simpler after differentiation and v as the part that becomes simpler after integration. In this case, we can choose u = x and v = sin5x.
Substitution can also be used to solve the integral of xcos5x dx. You can let u = 5x and du = 5dx, which will result in the integral becoming ∫(1/5)ucosu du.
Yes, the integral of the form ∫xcos(ax) dx, where a is a constant, can be solved using integration by parts or substitution. Both methods will yield the same result, but one may be easier to use depending on the specific integral.
The final answer is ∫xcos5x dx = (1/5)xsin5x + (1/25)cos5x + C, where C is the constant of integration.