Hello, I have a few questions! I need clarification on certain points that were not very clear in my calculus book.(adsbygoogle = window.adsbygoogle || []).push({});

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Question 1:

I know that [tex] \int e^{ax} dx = \frac{1}{a} e^{ax} [/tex]

But how do you integrate [tex] \int e^{ax^2} dx [/tex]?

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Question 2:

I know that integrating by parts is [tex] \int (something) dx= uv - \int vdu [/tex]

But what if there is a range?

If it is [tex] \int_{a}^{b} (something) dx [/tex] does it equal [tex] \left[ uv \right]_{a}^{b} - \int_{a}^{b} vdu [/tex] or does it simply equal [tex] uv - \int_{a}^{b} vdu [/tex]?

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Question 3:

How do you integrate [tex] \int log_ax dx [/tex] and [tex] \int e^{ln|secx|} dx [/tex].

In fact, is [tex] e^{ln|secx|} [/tex] reducable?

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Question 4:

I was taught that arcsinx exist only in the range [tex] \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] [/tex] and [tex] \left[ \frac{\pi}{2}, \frac{3\pi}{2} \right] [/tex] (I think because it fails the horizontal test if it isn't in those ranges)

If so, is it possible to integrate [tex] \int_{0}^{\pi} xarcsinx dx [/tex]? (If it is possible, is it because it isn't simply arcsinx but xarcsinx?)

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Question 5:

I am having a lot of problems integrating fuctions with exponents etc that have complex roots. My elementary calculus is shaky at best and I'm taking Advanced Engineering Mathematics (Kreyzig) - I have to. Can anyone recommend me any links or books that may help me?

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Reply to HallsofIvy:

Thank you for your reply! I have a question about your reply on question 1: In my Adv Eng Maths (Kreyzig) book, one of the questions is how to integrate [tex] \int xe^{x^2/2} [/tex] and the answer is [tex] e^{x^2/2} + C [/tex] but I don't understand how to do it!

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# Integrating Exponentials with Roots that have Roots? (And other small Q's)

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