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I’ve got this tricky trig substitution that I’ve been trying to do as for my Calc II class. I think that I’ve done the substitution part right I just have no idea where to go from here. I’ve tried many routes including integrating by parts as well.

Please help me thank you

1.) Original question = ∫e^x * √(1+e^2x ) dx

2.) after trig substitution = ∫tanθ *[sec〗^3 θdθ

I have looked at another source for help with I believe an identical question and it integrates this and it gives me

3.) (〖sec〗^3 θ)/3 + C

So I guess all I’m really asking is how they got from step two to step three.

Please help me thank you

1.) Original question = ∫e^x * √(1+e^2x ) dx

2.) after trig substitution = ∫tanθ *[sec〗^3 θdθ

I have looked at another source for help with I believe an identical question and it integrates this and it gives me

3.) (〖sec〗^3 θ)/3 + C

So I guess all I’m really asking is how they got from step two to step three.

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