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Grade 12Integral Calculus

evaluate
∫ 1 /((a)^x (b)^x) dx

taniska

12 Years agoGrade 12

1 Answer

Jitender Singh

12 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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