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 an anti derivative (or integral) of the following function by the method of inspection.
sin 2x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 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:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
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:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
`int (dx)/(sin^2x cos^2x) dx` equals
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`int (dx)/(x(x^2 + 1))` equals
`int x^2 e^(x^3) dx` equals
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
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)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
What is “an integral of \(f\)” ?
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 \[\int \text{cosec}^2 x\,dx\]
Evaluate \[\int \frac{dx}{1+x^2}\]
Evaluate \[\int e^x\,dx\]
Evaluate \[\int a^x\,dx\]
