Advertisements
Advertisements
प्रश्न
Find the following integrals:
`int(sec^2x)/(cosec^2x) dx`
Advertisements
उत्तर
Let `I = int (sec^2 x)/(cosec^2) dx`
`I = int (1/(cos^2 x))/(1/(sin^2 x)) dx`
`I = int (sin^2 x)/(cos^2 x)` dx
`I = int tan^2 x dx`
`I = int sec^2 x - 1 dx`
`I = int sec^2 x dx - int 1 dx`
I = tan x - x + C
APPEARS IN
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
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.
Cos 3x
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:
`intx^2 (1 - 1/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(1 - x) sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) 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/(sqrt(x+a) + sqrt(x+b))`
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:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log 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:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the function:
`sqrt((1-sqrtx)/(1+sqrtx))`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (dx)/sqrt(9x - 4x^2)` equals
`int (xdx)/((x - 1)(x - 2))` equals
`int e^x sec x(1 + tanx) dx` equals
`int sqrt(1 + x^2) dx` is equal to
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
