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Find value of int (ax+b)^(3//2) dx....

Find value of `int (ax+b)^(3//2) dx`.

Text Solution

Verified by Experts

Substitute `(ax+b)=z` in the given function.
Also,` (d)/(dx)(ax+b)=(dz)/(dx)`
or ` " " a=(dz)/(dx)`
`:. " " dx=(dz)/(a)`
and ` int (ax+b)^(3//2)dx= int z^(3//2) xx (dz)/(a)`
`=(1)/(a) int z^(3//2)dz`
=`(1)/(a)(z^(((3)/(2)+1)))/(((3)/(2)+1)) +c`
`=(1)/(a)(z^(5//2))/(5//2)+c`
Substitute back for z, we get
`int (ax+b)^(3//2) dx=(2)/(5a)(ax+b)^(5//2) +c`
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