evaluate following indefinite integrals a int

Question

Evaluate following indefinite integrals.

 (a) ∫ 5t ³ -10t -6 + 4 dt

 (b) ∫ dy

Solution

 (a) ∫ 5t ³ -10t -6 + 4 dt

There's not whole lot to do here other than use the two formulas.  Remember that while integrating powers (which aren't -1 of course) we just add one onto the exponent & then divide through the new exponent.

∫ 5t ³ -10t -6 + 4 dt = 5 ( ¼)  t ⁴  -10 ( 1/-5) t ^-5 + 4t + c

= 5/4 t ⁴ + 2t ^-5 + 4t + c

Be careful while integrating negative exponents.  Always remember to add one onto the exponent. 

(b) ∫ dy

∫ dy = ∫1dy = y + c

In this case we are actually just integrating a one!