Please solve Q Evaluate : ∫x2-1xx4+3x2+1dx - Maths - Integrals

Question

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Q Evaluate :
∫ x 2 - 1 x x 4 + 3 x 2 + 1 d x

Aarushi Mishra · Accepted Answer

∫x2-1xx4+3x2+1dx=∫x2-1xx2x2+3+1x2dx=∫x2-1x2x2+3+1x2dx=∫x2-1x2x2+2+1x2+1dx=∫x2-1x2x2+2×x×1x+1x2+1dx=∫1-1x2x+1x2+1dxLet u=x+1xdy=1-1x2I=∫1t2+1dtUse ∫1x2+a2dx=ln  x+x2+a2+cI=ln  t+t2+1+c=ln  x+1x+x+1x2+1+c

Please solve Q. Evaluate : ∫ x 2 - 1 x x 4 + 3 x 2 + 1 d x

Please solve
Q. Evaluate :
$\int \frac{x^{2} - 1}{x \sqrt{x^{4} + 3 x^{2} + 1}} d x$