Advertisements
Advertisements
प्रश्न
Integrate the function:
f' (ax + b) [f (ax + b)]n
Advertisements
उत्तर
Let = ∫ f'(ax + b).[f(ax + b)]n dx
Put f(ax + b) = t
∴af'(ax + b) dx = dt
∴ `I = 1/a int t^n dt = 1/a (t^(n + 1))/(n + 1) + C`
`= 1/((n + 1)a) [f (ax + b)]^(n + 1) + C`
APPEARS IN
संबंधित प्रश्न
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/(sin^2x cos^2x) dx` equals
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/sqrt(9x - 4x^2)` equals
`int x^2 e^(x^3) dx` equals
`int e^x sec x(1 + tanx) dx` equals
`int sqrt(1 + x^2) dx` is equal to
What is anti derivative of `e^(2x)`
`d/(dx)x^(logx)` = ______.
In \[\int f(x)\,dx\], what is \(x\) called?
What is “an integral of \(f\)” ?
What is integration?
Evaluate \[\int \cos x\,dx\]
Evaluate \[\int \sec^2 x\,dx\]
Evaluate \[\int \sec x\tan x\,dx\]
Which expression is an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Which expression is also an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
