its a hard question

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its a hard question

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let cosx = t

-sinxdx = dt ,limit from 1 to -1

integral from 1 to -1 [-e^t][2sint/2 + 3cost/2]dt

integral from -1 to 1 {[e^t][2sint/2 + cost/2] + [e^t][2cost/2]}dt

integral e^x[f(x) + f '(x)] = e^x*f(x)

[2sint/2*e^t]limit from -1 to 1 + integral from -1 to 1 [e^t][2cost/2]dt

2sin1/2*e^1 + 2sin1/2*e^-1 + [4/3cost/2*e^t +2/3sint/2*e^t]limit from -1 to 1

4/3cos1/2(e^1 - e^-1) + 8/3sin1/2(e^1 + e^-1)