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- We will do anything!
- You have defied my laws!
- Please forgive us!
- Well, we must find u and du in order to even begin. So, u is equal to 3x^4+1 and du/12x^3=dx. Now we are able to substitute.
- They will never understand with their peasant teachings
- Alright then, solve 36x^3(3x^4+1)^3 dx
- We can substitute u and du into the equation, and 36x^3 and 12x^3 can be simplified. After we can now add one to the exponent and divide by the exponent, then we can put what u was equal to back in to the equation and add C.
- So the answer is 3/4(3x^4+1)^4+C
- What if you challenge them with math?
- When you get to 1/u in the equation, you can change in to the natural log. Therefore the answer is ln|4x^4-5|+C
- Let me try, what is 16x^3/4x^4-5 dx
- How did they know that?
- Well in this equation, u=(4x^4-5) and du/16x^3=dx
- That was too easy!
- Well u is equal to 5x^2-l and du/10x is equal to dx
- You're annoying me!
- So the answer must be 3e^5x^2-1 + C
- Try 30xe^5x^2-1 dx
- Solve, 20x^4sec^2(2x^5-1) dx
- So I hope that the answer is 2tan(2x^5-1) + C
- How is this possible?
- This is a hard one! Well, u=2x^5-1 and du/10x^4=dx
- Fine, this is the last equation.
- How?!
- Thank you so much!
- I am an honorable man and must let you live
- Good thing Mrs.Stone taught us an not Sheldon
- How is this possible?!
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