Home
Class 12
MATHS
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

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INDEFINTE INTEGRAL

    FIITJEE|Exercise MATCH THE COLUMNS|6 Videos

  • INDEFINTE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • INDEFINTE INTEGRAL

    FIITJEE|Exercise COMPREHENSIONS= II|1 Videos

  • HYPERBOLA

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • MATHEMATICAL REASONING

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-2|18 Videos

Similar Questions

Explore conceptually related problems

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

inte^(x)[f(x)+f'(x)]dx=

inte^(x).[f(x)-f''(x)]dx=

Evaluate: int e^(x)(f(x)+f'(x))dx=e^(x)f(x)+C

Integration of form e^(x)(f(x)+f'(x))dx

Integration of the form f'(x)/(f(x))dx

Show that int e^(x)[f(x)+f'(x)]dx=e^(x).f(x)+c Hence, evaluate: int e^(x)((2+sin2x)/(1+cos2x))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)(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 = __________.