Question

Find : $\mathrm{\int \frac{x^{4}+1}{x^{6}+1}dx}$​

Answer 1

Step I:

we shall rationalize the given expression by multiplying and dividing with (${x}^{2}+1$)

Step II:

then the terms are separeted to form two different quantity such that in each case like terms will be cancelled and we get an easy form of the fraction.

Step III :

Now one of the fraction is easily the diffretial part of tan inverse and another is converted to it by multiplying and dividing with 3 and replacing ${x}^{3}\:as\:'t'$ .

The whole solution is in the attachments.

Refer to the attachments please.

Answer 2

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