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
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int (log x)/(log ex)^2` dx = _________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int cot^2x "d"x`
`int(log(logx))/x "d"x`
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
