Question

Which of the following is the answer to ∫x2sin(3x) dx? Hint: Do not integrate directly. Differentiate and check.

Answer 1

we have the expression

`\int x^2sin(3x)dx=-(1)/(3)x^2cos(3x)+(2)/(27)(3xsin(3x)+cos(3x))+C`

Rewrite the solution

`(2)/(9)xsin(3x)-((1)/(3)x^2-(2)/(27))(cos(3x)+C`

therefore

The answer is the first option