Howell Maxwell
08/22/2023 · High School
\( \int \frac { x ^ { 3 } + x ^ { 2 } + 1 } { x ( x - 1 ) ( x ^ { 2 } + x + 1 ) ( x ^ { 2 } + 1 ) ^ { 3 } } d x \)
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The integral \( \int \frac { x ^ { 3 } + x ^ { 2 } + 1 } { x ( x - 1 ) ( x^2 + x + 1 ) ( x^2 + 1 ) ^ { 3 } } d x \) is solved using partial fraction decomposition. The coefficients \(A, B, C, D, E, F, G\) are found by substituting convenient values for \(x\). The integral is then expressed as a sum of simpler integrals, which are integrated term by term to obtain the final result.
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