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STATEMENT-1 : intx^(x)(1+logx)dx=x^(x)+C...

STATEMENT-1 : `intx^(x)(1+logx)dx=x^(x)+C`
and
STATEMENT-2 : `(d)/(dx)x^(x)=x^(x)(1+logx)`

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explantation for Statement-1

B

Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explantation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

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Knowledge Check

  • (d)/(dx)((x^(2))/(x-1))=

    A
    `1+(1)/((x-1)^(2))`
    B
    `(1)/((x-1)^(2))-1`
    C
    `1-(1)/((x-1)^(2))`
    D
    `(-1)/((x-1)^(2))`

  • (d)/(dx)((logx)/(x^(2)))=

    A
    `x^(-2)(1+2logx)`
    B
    `x^(-2)(2logx-1)`
    C
    `x^(-3)(1-2logx)`
    D
    `x^(-4)(1-2logx)`

  • (d)/(dx)[sin^(-1)((2^(x+1))/(1+4^(x)))]

    A
    `(1)/(sqrt(1-2^(x)))`
    B
    `(log)/(sqrt(1-4^(x)))`
    C
    `(2^(x+1)log2)/(1+4^(x))`
    D
    `(log2)/(sqrt(1-2^(x)))`

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