Question

integrate x to the power 4 by X square + 1 DX

Answer 1

Answer :

Now, ∫ x⁴/(x² + 1) dx

= ∫ (x² + 1 - 1)²/(x² + 1) dx

= ∫ {(x² + 1)² - 2(x² + 1) + 1}/(x² + 1) dx

= ∫ (x² + 1)²/(x² + 1) dx - 2 ∫ (x² + 1)/(x² + 1) dx

+ ∫ 1/(x² + 1) dx

= ∫ (x² + 1) dx - 2 ∫ dx + ∫ 1/(x² + 1) dx

= x³/3 + x - 2x + tan⁻¹x + c [c = integral constant]

= x³/3 - x + tan⁻¹x + c

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