Advertisements
Advertisements
Question
Evaluate: `int 1/(sqrt("x") + "x")` dx
Advertisements
Solution
Let I = `int 1/(sqrt("x") + "x")` dx
`= int 1/(sqrt"x" (1 + sqrt"x"))` dx
Put `1 + sqrt"x"` = t
∴ `1/(2sqrt"x") "dx"` = dt
∴ `1/sqrt"x" "dx"` = 2 dt
∴ I = `int (2 * "dt")/"t"`
`= 2 int 1/"t"` dt
= 2 log |t| + c
∴ I = 2 log `|1 + sqrt"x"|` + c
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
tan2(2x – 3)
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
