Home
Class 12
MATHS
cos^(3) x e^(log sinx)...

`cos^(3) x e^(log sinx)`

Text Solution

Verified by Experts

Let
`I=int cos^(3) x e^(log sinx) dx= int(cos x)^(3) sin x dx`
`( :' e^(log x)=x)`
`=-int (cos x)^(3) (-sin x) dx`
`" Let " cos x=t rArr -sin x dx =dt`
`:. I =- int t^(3) dt= -(t^(4))/(4)+C =- (cos^(4))/(4)+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.11|21 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

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

Similar Questions

Explore conceptually related problems

cos^3x e^(log sin x)

int_0^(pi/2) cos^3x e^(log_e sinx) dx=

int cos^(3)x.e^(log(sin x)) dx is equal to

If u=e ^(log cos 4x ),v =e ^(log sin 4x ),then (dv)/(du)=

If inte^(sinx).(xcos^(3)x-sinx)/(cos^(2)x)dx=e^(sinx)f(x)+C , such that f(0) =-1 then pi/3-f(pi/3) is equal to:

int_(0)^(pi//4)e^( sinx)(((x cos^(3)x- sinx))/( cos^(2)x))dx

int_(0)^(pi) cos 2x . Log (sinx) dx

lim_(xoto0) x log_(e) (sinx) is equal to