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1) why there is a square root sign and then a square? it is not clear.

2) Is that x^2 or x^4.

3)

4)

There is no simple answer to this... x^x = e^{x ln x} Expand this in power series. like e^x. So f9x) = 1 + x ln x + (x ln x)^2 /2 + (x ln x)^3 / 6 + .... Try integrating each term separately. Even those integrals are not easy to obtain.. It is simpler to evaluate definite integrals with x ranging fro m 0 to 1.. and indefinite integral is not easy to find.

5) put cos x = y. so - sinx dx = dy. then, integral of - Cos y dy = - Sin y = - Sin (cosx) + K

the first question too.. u write differently.. i did not get it.. please write answer again for them, i suppose u have the answers saved with you somewhere..