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verify that int(2x-1)/(2x+3)dx = x - log...

verify that `int(2x-1)/(2x+3)dx = x - log|(2x+3)^(2)|+C`

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The correct Answer is:
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Let `I = fint(2x-1)/(2x+3)dx = int(2x+3-3-1)/(2x+3)dx`
`=int1dx-4int(1)/(2x+3)dx x- int(4)/(2(x+3/2))dx`
` =x-2log+|(x+3/2)|C'=x-2|((2x+3)/(2))|+C'`
`=x - 2log|(2x+3)|+2log2+C'[:'log'(m)/(n)=logm-logn]`
`=x-log|(2x+3)^(2)|+C, [:'C = 2log2+C]`
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  • int(1)/(2x+log(x^(x)))dx=

    A
    `(log2).log(logx)`
    B
    `log(2+logx)`
    C
    `log(2.logx)`
    D
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  • inte^(3x)(log2x+(1)/(x))dx=

    A
    `(e^(3x))/(3)log2x+c`
    B
    `(e^(3x))/(2)log2x+c`
    C
    `3e^(3x)log2x+c`
    D
    `e^(3x)log2x+c`

  • If int(4x+1)/(x^(2)+3x+2)dx =a log |x+1|+blog |x+2| +C , then

    A
    a = b
    B
    a + b =4
    C
    a = 2b
    D
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