Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
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 :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find : `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(1 + cot x)`
Solve: dy/dx = cos(x + y)
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
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\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).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 dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
`int logx/(log ex)^2*dx` = ______.
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int cos sqrtx` dx = _____________
`int cos^7 x "d"x`
`int(log(logx))/x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int dx/(1 + e^-x)` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
`int x^3 e^(x^2) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
