Advertisements
Advertisements
Question
Evaluate : `∫1/(3+2sinx+cosx)dx`
Advertisements
Solution
let I=`∫1/(3+2sinx+cosx)dx`
put `tan(x/2)=t`
`x=2tan^-1t`
`dx=(2dt)/(1+t^2)` and `sinx=2t/(1+t^2), cosx((1-t^2)/(1+t^2))`
`therefore I=tan^-1[tan(x/2)+1]+c`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`(1+ log x)^2/x`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int dx/(1 + e^-x)` = ______
`int sec^6 x tan x "d"x` = ______.
`int cos^3x dx` = ______.
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
