U-Substituition
When taking the integral of a complex function, using U-substitution can help take apart the function in order to solve for the integral.
To start off, choose the best part of the function to be "u". t^3 would be the best option for "u". Then you take the derivative of "u" in order to get du/dt. Next you separate du and dt. You should now have du= 3t^2 dt. Now that you have the derivative of "u", you substitute t^3 out of the original function in the integral, putting in "u". The integral now would have the function of 3t^2(cos(u))dt. Also, notice that this function has 3t^2 dt and so does the derivative of "u", du. You can substitute the 3t^2 dt for du which is no what is also equals. The function now looks like the integral of cos(u)du. This is now easier to take the integral of and would be sin(u) + C. (C is the constant that could be there due to the fact that taking the derivative of a constant, it equals zero.) Finally you can put the value that equaled "u", t^3, making the solution of the integral, sin(t^3) + C =y
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