Home
Class 12
MATHS
Evaluate: inte^x\ ((1+sinx)/(1+cosx))\ d...

Evaluate: `inte^x\ ((1+sinx)/(1+cosx))\ dx`

Text Solution

Verified by Experts

` int((1+sin x)/(1+cos x))e^(x) dx`
`=int((1+2sin .(x)/(2) cos .(x)/(2))/(2cos^(2).(x)/(2))) e^(x) dx`
` =(1)/(2) int e^(x) sec^(2) .(x)/(2) dx+ int e^(x) tan.(x)/(2) dx`
`=(1)/(2) int e^(x) sec^(2) .(x)/(2) dx+ tan.(x)/(2) int e^(x) dx`
` - int {(d)/(dx) tan .(x)/(2) int e^(x) dx} dx+C`
`=(1)/(2) int e^(x) sec^(2) .(x)/(2) dx+ e^(x) tan.(x)/(2)`
`=e^(x) tan.(x)/(2) +C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.7|11 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.8|6 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int e^x ((1+sinx)/(1+cosx))dx=

Evaluate int e^(x)((1-sinx)/(1-cosx))dx.

Evaluate: int_0^(pi/2)(x+sinx)/(1+cosx) dx

Evaluate: inte^x\ (cosx-sinx)\ dx

Evaluate : int {(1+sinx)/(x-cosx)}dx .

Evaluate: int(1+sinx)/(sqrt(x-cosx))dx

Evaluate: int(1+sinx)/(sqrt(x-cosx))dx

Evaluate: int(1+2xsinx-cosx)/(x(1-cosx))dx

int(x-sinx)/(1-cosx)dx

int(x-sinx)/(1-cosx)dx