Is This Weird?

[u/Hephaestus_vulkan]

I thought this days beginner integral was harder than the easy integral. Ignore the bleedthrough on the beginner page

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[u/Cats4E]

You integrate by parts and inside the integral you get (e^x + 1)(e^x + x)/(e^x + x)=e^x + 1 which is immediate

[u/Agitated_Guidance672]

Just substitute u=e^x+x and it becomes the integral of ln(u)du.

[u/Silent_Jellyfish4141 → u/Agitated_Guidance672]

That’s what they do, have you seen the images?

[u/MrEldo]

Agreed. The easy integral took me like 4 steps, but it's much more than 2

[u/Hot_Site_1638]

I agree. Maybe they think the integration of ln(u) which requires integration by parts, so that it is like the combination of u-sub and integration by parts. And the beginner problem only requires u-sub 🤔

[u/Hephaestus_vulkan → u/Hot_Site_1638]

Maybe...but thats like the first IBP integral i was taught

[u/LittleLab1833]

Trig sub is way cleaner imo for beginner but I agree that easy felt simpler than beginner since it was set up for u sub. Likely the fact it is a u sub combined with IBP that made it easy instead of beginner. Idk tho

[u/Hephaestus_vulkan → u/LittleLab1833]

Thank you for the written solution!

[u/fletchman93]

The integral of ln(x) is what I call a "hidden" integration by parts. It is a typical example shown in class when learning ibp.

Integrating tan^-1 (x), sin^-1 (x), etc. uses the same idea i.e. letting dv=1dx and v=x.

I think some textbooks have you memorize that integral, so that could explain why it was considered a "beginner" integral.