MHB How can substitution make solving integrals easier?

[TheFallen018]

Hi, I've got this problem that I've been trying to work out. I think most of my problems come from the fact that I am not yet well versed in u substitution when it comes to integrals. I'm also not 100% sure what the problem is asking.

I've tried doing a couple of things, but they don't seem to be correct. I'm now at that point where everything I do confuses me more. If someone could help shed some light on the subject, I would be very grateful. Thanks.

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[Opalg]

Hi, I've got this problem that I've been trying to work out. I think most of my problems come from the fact that I am not yet well versed in u substitution when it comes to integrals. I'm also not 100% sure what the problem is asking.

I've tried doing a couple of things, but they don't seem to be correct. I'm now at that point where everything I do confuses me more. If someone could help shed some light on the subject, I would be very grateful. Thanks.

A couple of things to get you started:

In the suggested substitution, if $u = \dfrac{e^{5x}}5$ then $u^2 = \dfrac{e^{10x}}{25}.$ That should help you with the denominator of the integrand.

If $u = \dfrac{e^{5x}}5$ then $\dfrac{du}{dx} = e^{5x}.$ That should help convert the $dx$ in the integral to something involving $du$.