Indefinite Integration

Find:

    \[\int \sqrt{x^{4}+\frac{1}{x^{4}}+2}\,\textrm{d}x\]

Hint:

    \[\sqrt{x^{4}+\frac{1}{x^{4}}+2}=\sqrt{\left(x^{2}+\frac{1}{x^{2}}\right)^{2}}=x^{2}+\frac{1}{x^{2}}\]

    \[\int \sqrt{x^{4}+\frac{1}{x^{4}}+2}\,\textrm{d}x=\int \left(x^{2}+\frac{1}{x^{2}}\right)\,\textrm{d}x\]

Source: Vietnam I (Question 1, p. 8)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

Leave a Reply