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[tex] \int {(x^2 + 1)^{5/2}}x dx [/tex]

This is simple to integrate but the trigonometric function:

[tex] \int 3/5{(\sec x)}^{5/3}x dx [/tex] is already a problem.

The first gives:

[tex] \int {(x^2 + 1)^{5/2}}x dx = \int {u}^{5/2}1/2 du = 1/2 \int u^{5/2} du = 1/2 ({2u^{7/2}/7 + C) = 1/7{(x^2 + 1)}^{7/2} + C [/tex]

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# Elliptic integrals

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