Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
उत्तर
Let I = `int (2 cos x - 3 sin x)/(6 cos x + 4 sin x)` dx
`= 1/2 int (2 cos x - 3 sin x)/(3 cos x + 2 sin x)` dx
Put 3 cos x + 2 sin x = t
(- 3 sin x + 2 cos x) dx = dt
Hence, `I = 1/2 int 1/t` dt
`= 1/2 log abs t + C`
`= 1/2 log abs (3 cos x + 2 sin x) + C`
APPEARS IN
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
cot x log sin x
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3)dx`
Fill in the Blank.
To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int logx/x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int (1+x+x^2/(2!)) dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intxsqrt(1+x^2)dx`
