Advertisements
Advertisements
प्रश्न
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Advertisements
उत्तर
Let I = `int x^2 (1 - 1/x^2) dx = x^2 ((x^2 - 1)/x^2) dx`
`= int (x^2 - 1)` dx
`∴ int x^2 dx - int 1 dx`
`= x^3 /3 - x + C`
APPEARS IN
संबंधित प्रश्न
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
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`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) 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 (dx)/sqrt(9x - 4x^2)` equals
What is anti derivative of `e^(2x)`
If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.
`d/(dx)x^(logx)` = ______.
What is integration called because it reverses the operation of finding derivatives?
What is integration?
Which statement about indefinite integrals is correct?
Which antiderivative has derivative \(1\)?
Evaluate \[\int \sec^2 x\,dx\]
Evaluate \[\int \sec x\tan x\,dx\]
Evaluate \[\int \frac{1}{x}\,dx\]
