Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Advertisements
उत्तर
Let I = `int (1)/(4 + 3cos^2x).dx`
Dividing both numerator and denominator by cos2x, we get
I = `int (sec^2x)/(4sec^2 x + 3).dx`
= `int (sec^2x)/(4(1 + tan^2x) + 3).dx`
= `int (sec^2x)/(4tan^2x + 7).dx`
Put tan x = t
∴ sec2x dx = dt
I = `int dt/(4t^2 + 7)`
= `int dt/((2t)^2 + (sqrt(7))^2`
= `(1)/sqrt(7)tan^-1 ((2t)/sqrt(7)).(1)/(2) + c`
= `(1)/(2sqrt(7))tan^-1 ((2tanx)/sqrt(7)) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`x/(e^(x^2))`
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int cot^2x "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int sec^6 x tan x "d"x` = ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "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.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int1/(x(x-1))dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
