Question

Evaluate the definite integral.\ $int_{e}^{e^4} frac{1}{xln(x)} dx$ A) $ln(ln(e^4)) - ln(ln(e^1))$ B) $ln(e^4) - ln(e^1)$ C) 3 D) $ln(ln(4)) - ln(ln(1))$ E) $ln(4)$

          Evaluate the definite integral.\
$int_{e}^{e^4} frac{1}{xln(x)} dx$
A) $ln(ln(e^4)) - ln(ln(e^1))$
B) $ln(e^4) - ln(e^1)$
C) 3
D) $ln(ln(4)) - ln(ln(1))$
E) $ln(4)$

$Evaluate the definite integral.inte^e^4 frac1xln(x) dx A) ln(ln(e^4)) - ln(ln(e^1)) B) ln(e^4) - ln(e^1) C) 3 D) ln(ln(4)) - ln(ln(1)) E) ln(4)$

Added by Monica F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

08/06/2023

Step 1

It seems like the integral is: $$\int_1^e \ln(x) \, dx$$ Now, we can use integration by parts to evaluate this integral. Let $u = \ln(x)$ and $dv = dx$. Then, $du = \frac{1}{x} dx$ and $v = x$. Using integration by parts formula, $\int u \, dv = uv - \int v \, Show more…

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