Advertisements
Advertisements
प्रश्न
Evaluate:
Advertisements
उत्तर
\[\int\frac{dx}{a^x b^x}\]
\[ = \int\left( a^{- x} b^{- x} \right)dx\]
\[ = \frac{a^{- x} b^{- x}}{- \log_e \left( ab \right)} + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate `int_(-1)^2|x^3-x|dx`
Evaluate :
`∫_(-pi)^pi (cos ax−sin bx)^2 dx`
If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.
Evaluate: `intsinsqrtx/sqrtxdx`
Evaluate the integral by using substitution.
`int_0^1 x/(x^2 +1)`dx
Evaluate the integral by using substitution.
`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`
Evaluate the integral by using substitution.
`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`
Evaluate the integral by using substitution.
`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`
Evaluate the integral by using substitution.
`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`
`int 1/(1 + cos x)` dx = _____
A) `tan(x/2) + c`
B) `2 tan (x/2) + c`
C) -`cot (x/2) + c`
D) -2 `cot (x/2)` + c
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate of the following integral:
(i) \[\int x^4 dx\]
Evaluate:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?
If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals ______.
Evaluate the following:
`int "dt"/sqrt(3"t" - 2"t"^2)`
In Method: Resubstitution, what should be done first?
If the substitution is \[t=g(x)\], what differential relation is used in Method 2: Changing the Limits?
For the integral \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\], which substitution is suitable?
If \[t=\tan^{-1}x\], what is \[dt\]?
What is the value of \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\]?
