Advertisements
Advertisements
प्रश्न
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Advertisements
उत्तर
Let I = `int (x^3 + 3x + 4)/sqrtx` dx
`I = int (x^(5/2) + 3x^(1/2) + 4x^(-(1)/2))` dx
`I = int x^(5/2) dx + 3 int x^(1/2) dx + 4 int x^(-(1)/2) dx`
`I = 2/7 x^(7/2) + 3 xx 2/3 x^(5/2) + 4 xx 2x^(1/2) + C`
`I = 2/7 x^(7/2) + 2x^(3/2) + 8 sqrtx + C`
APPEARS IN
संबंधित प्रश्न
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 the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 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 - 3cos x + e^x) dx`
Find the following integrals:
`intsec x (sec x + tan x) 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/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
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:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`sqrt((1-sqrtx)/(1+sqrtx))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/(sin^2x cos^2x) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equal
`int (xdx)/((x - 1)(x - 2))` equals
`int sqrt(1 + x^2) dx` is equal to
`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 ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
In \[\int f(x)\,dx\], what is \(f(x)\) called?
What is integration?
Evaluate \[\int \sec^2 x\,dx\]
Which expression is an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Evaluate \[\int \frac{dx}{1+x^2}\]
Evaluate \[\int e^x\,dx\]
Evaluate \[\int \frac{1}{x}\,dx\]
