\( \int \frac{2 x\left(1+2 x^{2}\right)}{\left(1+x^{2}+x^{4}\right)} d

1.	\( \int \frac{2 x\left(1+2 x^{2}\right)}{\left(1+x^{2}+x^{4}\right)} d x \) is equal to:-
Answer» Let I = \(\int\cfrac{2x(1+2x^2)}{1+x^2+x^4}dx\) Let 1 + x² + x⁴= t = (2x + 4x³)dx = dt = 2x(1 + 2x²) dx = dt \(\therefore\) I = \(\int\cfrac{dt}t\) = log t + c = log\|1 + x² + x⁴ \| + c

\( \int \frac{2 x\left(1+2 x^{2}\right)}{\left(1+x^{2}+x^{4}\right)} d x \) is equal to:-

Answer»

Let I = \(\int\cfrac{2x(1+2x^2)}{1+x^2+x^4}dx\)

Let 1 + x² + x⁴= t

= (2x + 4x³)dx = dt

= 2x(1 + 2x²) dx = dt

\(\therefore\) I = \(\int\cfrac{dt}t\) = log t + c

= log|1 + x² + x⁴ | + c

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\( \int \frac{2 x\left(1+2 x^{2}\right)}{\left(1+x^{2}+x^{4}\right)} d x \) is equal to:-

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