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Integral Calculus HELP PLZ (1 Viewer)

Drdusk

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Please view image attached. Answers have been written in red.

Thanks!!!
There's different ways you can do a)

You can change to which after expanding will give you an integral with varying powers of (1+x) which you can integrate straight away.

You can also do a u sub by letting and then expanding to get varying powers of which you can also integrate straight away.
 

Trebla

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For the first one, you can use the substitution u=x+1.

For the second one, you will need to differentiate both sides of the substitution with respect to x and use the chain rule





You can then substitute x dx and all the remaining components with x's from there.
 

idkkdi

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There's different ways you can do a)

You can change to which after expanding will give you an integral with varying powers of (1+x) which you can integrate straight away.

You can also do a u sub by letting and then expanding to get varying powers of which you can also integrate straight away.
by the second statement he probably means x = sin^2 u
 

Drdusk

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Part two would be done as so



















I suggest going to the textbook and learning how to do u sub integrals because they can get harder from here. I've done it step by step here so you can understand how to do them but you can cut down a few lines.
 

Drongoski

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1)


Evaluating the definite integral will yield: 1696/105
 
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Drongoski

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Q2


Evaluating the definite integral will yield: 64/15
 
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