Advertisements
Advertisements
Question
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Advertisements
Solution
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
RELATED QUESTIONS
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`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
sin 2x
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 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:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 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`
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
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:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/(x(x^2 + 1))` equals
`int sqrt(1 + x^2) dx` is equal to
What is anti derivative of `e^(2x)`
`d/(dx)x^(logx)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
