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evaluate ∫ 1 /((a)^x (b)^x) dx

evaluate 
∫ 1 /((a)^x (b)^x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1}{a^{x}b^{x}}dx
I = \int \frac{1}{(ab)^{x}}dx
I = \int (ab)^{-x}dx
t = -x
dt = -dx
I = -\int (ab)^{t}dt
I = \frac{-(ab)^{t}}{log(ab)} + constant
I = \frac{-(ab)^{-x}}{log(ab)} + constant
I = \frac{-(ab)^{-x}}{log(a)+log(b)} + constant

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