Advertisements
Advertisements
प्रश्न
Evaluate: `int 1/(sqrt("x") + "x")` dx
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int cos^7 x "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
What is integration by substitution?
Which standard substitution is used for \[\sqrt{x^2-a^2}\], \[\frac{1}{\sqrt{x^2-a^2}}\], or \[x^2-a^2\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
