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_0^4(|x|+|x-2|+|x-4|)dx`
Evaluate the integral by using substitution.
`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)
Evaluate the integral by using substitution.
`int_0^2 dx/(x + 4 - x^2)`
The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.
`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 of the following integral:
(i) \[\int x^4 dx\]
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate the following definite 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 each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
`int_0^1 x(1 - x)^5 "dx" =` ______.
`int_0^(pi4) sec^4x "d"x` = ______.
Find: `int (dx)/sqrt(3 - 2x - x^2)`
In Method: Resubstitution, what should be done first?
After finding the antiderivative in Method: Resubstitution, what is the next step?
If the substitution is \[t=g(x)\], what differential relation is used in Method 2: Changing the Limits?
Under Method: Changing the Limits, what does the lower limit \[a\] become?
If \[t=\tan^{-1}x\], what is \[dt\]?
After using \[t=\tan^{-1}x\] in \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\], which integral results?
What is the value of \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\]?
