Calculus: Evaluate the indefinite integral and simplify your answer - ∫t^2e^2t^3 dt?
∫t^2e^2t^3. I know the answer is 1/6e^2t^3+C. My problem is how to show the work. Can anyone explain this to me so I won't get points taken off for not showing work? This is exactly how the problem is. There are no parenthesis. Not really sure if this is the best way to type it in. The problem reads the intergral of t squared times e to the power of 2t cubed. I am not good at calculus so I need help not criticism (yes there are people on here that are mean spirited). Thanks in advance. It is greatly appreciated.
∫t^2e^2t^3. I know the answer is 1/6e^2t^3+C. My problem is how to show the work. Can anyone explain this to me so I won't get points taken off for not showing work? This is exactly how the problem is. There are no parenthesis. Not really sure if this is the best way to type it in. The problem reads the intergral of t squared times e to the power of 2t cubed. I am not good at calculus so I need help not criticism (yes there are people on here that are mean spirited). Thanks in advance. It is greatly appreciated.
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- ∫t^2 e^(2t^3) dt
let e^(2t^3) = u
6t^2 e^(2t^3) dt = du
t^2 e^(2t^3) dt = du/6
- 1/6 ∫ du
= - (1/6) u + C
= - (1/6) e^(2t^3) + C
let e^(2t^3) = u
6t^2 e^(2t^3) dt = du
t^2 e^(2t^3) dt = du/6
- 1/6 ∫ du
= - (1/6) u + C
= - (1/6) e^(2t^3) + C