Integral question

[NoxDeus]

∫ e^(3x)√(1+9x⁴) dx
Hi, I need help with the above question. I don't think it can be solved by substitution method and I tried solving via by parts but I'm stuck in a loop because of the e^3x and the sqrt. Any other idea?
By the way, the full question is f(x) = ∫e^(3t)√(1+9t⁴) dt with upper limit x and lower limit 0.

 

[Dr.Peterson]

Please show your work by parts, so we can see what went wrong. Sometimes loops occur but can be escaped; or you may be making a mistake in the process (e.g. choosing unhelpful parts).

 

[Steven G]

I would 1st let u = 3t so that du/3 = dt and 1+ 9t^4 = 1+9(u/3)^4= 1+ u^4/9 = 1+ (u^2/3)62. This way the power of e is simply u and you should not have a loop.

 

[pka]

What are the instructions? If \(\displaystyle f(x) = \int_0^x {{e^{3t}}\sqrt {1 + 9{t^4}} dt} \) Could it ask for \(f^{\prime}(x)~?\) the derivative.