Advertisements
Advertisements
प्रश्न
Evaluate the following.
`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 : `int (sinx)/sqrt(36-cos^2x)dx`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
`int sqrt(1 + "x"^2) "dx"` =
`int x^x (1 + logx) "d"x`
`int(log(logx))/x "d"x`
`int x^3"e"^(x^2) "d"x`
`int dx/(1 + e^-x)` = ______
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
What is integration by substitution?
Which standard substitution is used for \[\sqrt{x^2-a^2}\], \[\frac{1}{\sqrt{x^2-a^2}}\], or \[x^2-a^2\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?
For indefinite integrals, what should be done after integration in the new variable?
