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We have to find the integral of but first we will convert this trigonometric function into algebraic function by substitution which is,

Put ex = t, so, = ex,

Hence ex dx = dt, putting in the function we get,

I = We will solve this function by using partial fractions. A(t + 2)(t - 1) + B(t + 2) + C(t - 1)2 = t01 + t10 + t20

At2 + At - 2A + Bt + 2B + Ct2 + C – Ct = t01 + t10 + t20

A + C = 0, A + B – C = 0, –2A + 2B + C = 1

B = 2C, 2C + 4C + C = 1,

C = , A = , B = Now making a function into partial fractions, we get,

I = I = ln  ln + C

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