Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of
Write a value of
Write a value of
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
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 : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int 1/(cos x - sin x)` dx = _______________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int cot^2x "d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int x^3"e"^(x^2) "d"x`
`int dx/(1 + e^-x)` = ______
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int1/(x^2+4x-5)dx`
If \[x=g(t)\] and \[dx=g'(t)dt\], which formula represents integration by substitution?
Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
