Find $\int _ { 0 } ^ { 1 } \frac { \ln \left( x ^ { 2 } \right) } { x } d x$
A) 0
B) 1
C) 1/2
D) Divergent

Name: Find $\int _ { 0 } ^ { 1 } \frac { \ln \left( x ^ { 2 } \right) } { x } d x$ A) 0 B) 1 C) 1/2 D) Divergent
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Question

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The integral $\int _ { 0 } ^ { 1 } \frac { \ln \left( x ^ { 2 } \right) } { x } d x$ diverges because the integrand becomes infinite as $x$ approaches 0. Specifically, $\frac{\ln(x^2)}{x}$ behaves like $\frac{-\infty}{x}$ near 0, leading to a non-convergent integral.

Find ∫01ln⁡(x2)xdx\int _ { 0 } ^ { 1 } \frac { \ln \left( x ^ { 2 } \right) } { x } d x∫01​xln(x2)​dx

Find $\int _ { 0 } ^ { 1 } \frac { \ln \left( x ^ { 2 } \right) } { x } d x$