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evaluate the following integral ∫ (e^(x – 1) + x^(e – 1)) / e^x + x^e dx

evaluate the following integral
∫ (e^(x – 1) + x^(e – 1)) / e^x + x^e dx

Grade:12

1 Answers

Sanjeev Kumar
24 Points
9 years ago
let e^x + x^e = t
e^x + ex^e dx = dt 
e{e^(x – 1) + x^(e – 1)}dx = dt
{e^(x – 1) + x^(e – 1)} dx = dt/e
equating the above value in the question, we get
∫dt/e × t
= 1/e∫dt/t
= 1/e log t
= 1/e log (e^x + x^e)

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