Advertisements
Advertisements
प्रश्न
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Advertisements
उत्तर
We know that,
`d/dx` (ax + b)2 = 3a (ax + b)2
`=> (ax + b)^2 = 1/(3a) d/dx (ax + b)^3`
or (ax + b)2 = `d/dx[1/(3a) (axee + b)^3]`
Hence, the antiderivative of (ax + b)2 is `1/(3a)`(ax + b)3.
APPEARS IN
संबंधित प्रश्न
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.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int (ax^2 + bx + c) 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 (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
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:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
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:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int tan^(-1) sqrtx dx`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/(sin^2x cos^2x) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equals
`int (xdx)/((x - 1)(x - 2))` equals
`int sqrt(1 + x^2) dx` is equal to
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
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 ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
