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
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int(1 - x) sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`int(sec^2x)/(cosec^2x) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/sqrt(9x - 4x^2)` equal
`int e^x sec x(1 + tanx) dx` equals
What is “an integral of \(f\)” ?
What is integration?
What is \(C\) called in \[\int f(x)\,dx=F(x)+C\]?
Which statement about indefinite integrals is correct?
Which antiderivative has derivative \(1\)?
Evaluate \[\int \sin x\,dx\]
Evaluate \[\int \sec^2 x\,dx\]
Evaluate \[\int \text{cosec}^2 x\,dx\]
Evaluate \[\int \frac{dx}{1+x^2}\]
Evaluate \[\int e^x\,dx\]
