Integrate the function f(x) where f(x)= x^2 +sin(x) + sin^2(x)

Answer: Integral= x³/3+ x/2 - cos(x) -1/4 sin(2x) + C Using the general rule that integrating xⁿ results in x⁽ⁿ⁺¹⁾/(n+1), x² integrates to x³/3.sin(x) is integrated to -cos(x)To integrate sin²(x), the double angle formula for cos(2x) is needed. As cos(2x)= cos²(x) - sin²(x) and cos²(x) + sin²(x)=1, cos(2x)= 1 - 2 sin²(x). Therefore, sin²(x)= 1/2 - 1/2 cos(2x). Therefore, the integral of sin²(x) is equal to x/2 - 1/4 sin(2x)- the chain rule can be used in reverse to integrate cos(2x).The question has not specified that the integral should be in between boundaries and therefore is an indefinite integral. A constant therefore should be added.