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int (mx^(m+2n-1)-nx^(n-1))/(x^(2m+2n)+2x...

`int (mx^(m+2n-1)-nx^(n-1))/(x^(2m+2n)+2x^(m+n)+1)dx` is equal to

A

`(-x^(m))/(x^(m+n)+1)+C`

B

`(-x^(n))/(x^(m+n)+1)+C`

C

`(-x^(n))/(x^(m+n)+1)+C`

D

`(x^(m))/(x^(m+n)+1)+C`

Text Solution

Verified by Experts

The correct Answer is:
c
Let `=int(mx^(m+2n-1)-nx^(n-1))/(x^(2m+2n)+2x^(m+n)+1)dx`. Then
`I=int((mx^(m+n)-n)x^(n-1))/((x^(m+n)+1)^(2))dx`
`rArrI=int((m+n)x^(m+2n-1)-nx^(m+2n-1)-nx^(n-1))/((x^(m+n)+1)^(2))dx`
`rArrI=int((m+n)x^(m+n-1)xxx^(n)-nx^(n-1)(x^(m+n)+1))/((x^(m+n)+1)^(2))dx`
`rArrI=intunderset(I)(x^(n))xx((m+n)x^(m+n-1))/(underset(II)((x^(m+n)+1)^(2)))dx-int(nx^(n-1))/((x^(m+n)+1))dx`
`rArrI=(-x^(n))/(x^(m+n)+1)-intnx^(n-1)xx(-1)/((x^(m+n)+1))dx-int(nx^(n-1))/((x^(m+n)+1))dx+C`
`rArrI=(-x^(n))/(x^(m+n)+1)+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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