Advertisements
Advertisements
Question
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Advertisements
Solution
`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
RELATED QUESTIONS
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/("x" log "x")`dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int logx/x "d"x`
`int (cos2x)/(sin^2x) "d"x`
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "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(1+x+(x^2)/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
