Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Advertisements
उत्तर
`int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
= `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)) xx (sqrt(7x - 2) + sqrt(7x - 5))/(sqrt(7x - 2) + sqrt(7x - 5)).dx`
= `int (3(sqrt(7x - 2) + sqrt(7x - 5)))/((7x - 2) - (7x - 5)).dx`
= `int (sqrt(7x - 2) + sqrt(7x - 5)).dx`
= `int(7x - 2)^(1/2) .dx + int(7x - 5)^(1/2).dx`
= `((7x - 2)^(3/2))/(3/2) xx (1)/(7) + ((7x - 5)^(3/2))/(3/2) xx (1)/(7) + c`
= `(2)/(21)(7x - 2)^(3/2) + (2)/(21)(7x - 5)^(3/2) + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int 1/(cos x - sin x)` dx = _______________
`int x/(x + 2) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
