Advertisements
Advertisements
प्रश्न
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Advertisements
उत्तर
Let I = `int (sqrtx - 1/sqrtx)^2 dx`
`I= int (x + 1/x - 2) dx`
`I = int x dx + int 1/x dx - 2 int 1 dx`
`I= x^2/2 + log abs x - 2x + C`
APPEARS IN
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
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.
e2x
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^2 - 3sinx + 5sqrtx) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
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/(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:
`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:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`int (dx)/(sin^2x cos^2x) dx` equals
`int x^2 e^(x^3) dx` equals
`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 ______.
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 ______.
What is integration?
Evaluate \[\int \cos x\,dx\]
Evaluate \[\int \sin x\,dx\]
Evaluate \[\int \sec^2 x\,dx\]
Evaluate \[\int \text{cosec}^2 x\,dx\]
Evaluate \[\int e^x\,dx\]
