Anti derivative & Integral almost go hand in hand.
Use the power rule for both the first & third expression. For the trigonometric expression, you must take the derivative of 22x which is 22. Then you must take the reciprocal of that which is 1/22 & put that outside of integral. Then you must remember that the anti derivative of a sine function is a negative cosine function.
Int(x^3 + sin 22x + (x+1)^3/4) dx =
(x^4)/4 - (1/22)cos 22x + (4/7)(x+1)^7/4 + C
