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evaluate ∫ { x^2 + e^(log x) + (e/2)^x} dx

evaluate
∫ { x^2 + e^(log x) + (e/2)^x} dx

Grade:12

1 Answers

kartik kumar
33 Points
9 years ago
I = ∫x2+elogx+(e/2)x dx
Let I1 = ∫x2 dx = x3/3 + C
     I2 = ∫elogx dx
 put, logx = t  ,after solving we find_
                                     I2= e2logx +C1
I3 =∫(e/2)x dx
put ,  (e/2)x = z
  or, log(e/2)x = logz
x.log(e/2) = logz
differentiate both side,
log(e/2)dx = (1/z)dz
now, I3 = ∫{z/log(e/2).z} dz 
I3 = 1/log(e/2)∫dz
I3 = z/log(e/2) + C2
I3 = (1/log(e/2)(e/2)x +C2
I = I1 + I2 + I3
I = x3/3 + e2logx+(e/2)x/log(e/2) +K

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