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Integration Question (1 Viewer)

SB257426

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I came across an integral that my teacher gave me to do. I have an answer but am unsure if my answer is correct. Other softwares (wolfram alpha and symbolab) are giving me different answers, but I suspect they are algebraically equivalent since they probably have different constants of integration.

Here is my answer:

Screen Shot 2023-03-12 at 7.11.17 pm.jpg

I would appreciate it if someone could verify this for me
 

tywebb

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There are other ways to write the answer like , etc., but whichever way you write it, it should have an inverse trig function.
 

tywebb

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Here are 2 methods.

Method 1 - trig substitution





Method 2 - rationalise the numerator






Notice this differs from the previous answer. However you can see that and differ by a constant by showing that and hence the 2 answers only differ by a constant.
 
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SB257426

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Here are 2 methods.

Method 1 - trig substitution





Method 2 - rationalise the numerator






Notice this differs from the previous answer. However you can see that and differ by a constant by showing that and hence the 2 answers only differ by a constant.
Thanks once again for your reply!!! I wanted to try a unique method so I did use rationalise the numerator instead of trig sub. Referring to my working l, I made a silly algebra mistake resulting to my answer. I attempted it once more and got your answer :)
 

Drongoski

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Here are 2 methods.

Method 1 - trig substitution





Method 2 - rationalise the numerator






Notice this differs from the previous answer. However you can see that and differ by a constant by showing that and hence the 2 answers only differ by a constant.
Got the same answer as in your Method-2, using almost the same approach. Didn't post as I was not sure if my answer was correct.
 
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s97127

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I came across an integral that my teacher gave me to do. I have an answer but am unsure if my answer is correct. Other softwares (wolfram alpha and symbolab) are giving me different answers, but I suspect they are algebraically equivalent since they probably have different constants of integration.

Here is my answer:

View attachment 37966

I would appreciate it if someone could verify this for me
There are a few integration solver on the internet with step by step instruction:


 

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