Advertisements
Advertisements
प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Advertisements
उत्तर
antiderivative of `(3sqrtx+1/sqrtx).=int (3sqrtx+1/sqrtx)dx`
Now, we have:
`int (3sqrtx+1/sqrtx)dx=int3x^(1/2)dx+intx^(-1/2)dx`
`=3xx2/3x^(3/2)+2x^(1/2)+c (`
`=2x^(3/2)+2x^(1/2)+C`
`=2sqrtx(x+1)+C`
Thus, the antiderivative of ` (3sqrtx+1/sqrtx). is 2sqrtx(x+1)+C` where c is the constant of integration
APPEARS IN
संबंधित प्रश्न
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 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 (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
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:
`sinx/(sin (x - a))`
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:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
`int (dx)/(sin^2x cos^2x) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equals
`int (xdx)/((x - 1)(x - 2))` equals
`int x^2 e^(x^3) dx` equals
`int e^x sec x(1 + tanx) dx` equals
What is anti derivative of `e^(2x)`
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
