The integral of (e^(2t))(25sint+20cost)dt can be solved using integration by parts, applied twice. The correct substitutions are u1 = 25sin(t) for the first integral and u2 = 20cos(t) for the second integral. The final solution is e^(2t)(14sint+3cost) + C, where C represents the constant of integration. This method allows for a systematic approach to solving complex integrals involving exponential and trigonometric functions.
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You could split the integral into two parts and work each one separately. I would start off with u1 = 25sin(t) for the first integral and u2 = 20cos(t) for the second one. Do similar substitutions the second time you apply integration by parts.mshiddensecret said:Homework Statement
Integrate: (e^(2t))(25sint+20cost)dt
Homework Equations
Integration by parts twice
The Attempt at a Solution
I don't know what to set for u and v.
I ended up wolfram alpha it but I want to know how to get there.
The solution is:
e^(2t)(14sint+3cost)=C
Should be + C, right?mshiddensecret said:e^(2t)(14sint+3cost)=C