Advertisements
Advertisements
Question
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Solution
`int tanx/(sec x + tan x)dx`
= `int tanx/(sec x + tan x) xx (secx - tanx)/(sec - tan x)dx`
= `int(sec x tan x - tan^2x)/(sec^2x - tan^2x)dx`
= `int(se c tan x - (sec^2x - 1))/(1)dx`
= `int sec x tan x dx - int sec^2 x dx + int 1 dx`
= sec x – tan x + x + c.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int \log_e x\ dx\].
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
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 (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
`int sqrt(1 + "x"^2) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int cot^2x "d"x`
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int(5x + 2)/(3x - 4) dx` = ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int 1/(sinx.cos^2x)dx` = ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int(1 + x + x^2/(2!) )dx`
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
`int1/(x^2 +4x-5)dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate:
`int(cos 2x)/sinx dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int1/(x(x - 1))dx`
