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Read the following passages and answer t...

Read the following passages and answer the following questions (7-9)
Consider the integrals of the form `l=inte^(x)(f(x)+f'(x))dx` By product rule considering `e^(x)f(x)` as first integral and `e^(x)f'(x)` as second one, we get `l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c`
`inte^(x)((1+sinxcosx)/(cos^(2)x))dx` is equal to

A

e^(x)f(x)+c`

B

`e^(x)tan^(2)x+c`

C

`e^(x)log|secx|+c`

D

none of these

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Read the following passages and answer the following questions (7-9) Consider the integrals of the form l=inte^(x)(f(x)+f'(x))dx By product rule considering e^(x)f(x) as first integral and e^(x)f'(x) as second one, we get l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c l=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx then l is equal to

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

  • Read the following passages and answer the following questions (7-9) Consider the integrals of the form l=inte^(x)(f(x)+f'(x))dx By product rule considering e^(x)f(x) as first integral and e^(x)f'(x) as second one, we get l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c int((1)/(lnx)-(1)/((lnx)^(2)))dx is equal to

    A
    `ln(lnx)+c`
    B
    `x+lnx+c`
    C
    `(x)/(lnx)+c`
    D
    none of these

  • inte^(x)[f(x)+f'(x)]dx=

    A
    `e^(x).f(x)+c`
    B
    `log[f(x)]+c`
    C
    `x.f(x)+c`
    D
    `x.e^(f(x))+c`

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    Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)(sin x + cos x)dx =

    Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)(x+1)dx = __________.

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