∫^ x
n dx = + CUsing the rule,
You can rewrite it as + C.
PROBLEM 2. Evaluate ∫ (5x^3 + x^2 − 6x + 4) dx.
Answer: We can break this up into several integrals.
∫ (5x
(^3) + x (^2) − 6x + 4) dx =
∫^5 x
(^3) dx +
∫^ x
(^2) dx −
∫^6 x dx + 4 ∫^ dx
Each of these can be integrated according to the Power Rule.
+ C + + C − + C + 4x + CThis can be rewritten as
+ − 3x^2 + 4x + CNotice that we combine the constant terms into one constant term C.
PROBLEM 3. Evaluate ∫(3 − x^2 )^2 dx.
Answer: First, expand the integrand.
∫ (9 − 6x
(^2) + x (^4) ) dx
Break this up into several integrals.
∫^9 dx − 6 ∫^ x
(^2) dx +
∫^ x
(^4) dx