Does this integral $\int _ { 0 } ^ { 1 }$ $\frac { 2 x ^ { 3 } } { \left( x ^ { 2 } + 4 \right) ^ { 2 } }$ dx = ln 5 - 2 ln 2 - $\frac { 1 } { 5 }$ ?

Question

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { 1 }$ $\frac { 2 x ^ { 3 } } { \left( x ^ { 2 } + 4 \right) ^ { 2 } }$ dx simplifies to ln 5 - 2 ln 2 - $\frac { 1 } { 5 }$ through a series of steps involving substitution and partial fraction decomposition, leading to the correct evaluation of the integral as stated.

Does This Integral ∫01\int _ { 0 } ^ { 1 }∫01​

Does This Integral $\int _ { 0 } ^ { 1 }$