Advertisements
Advertisements
Question
`int sqrt(1 + "x"^2) "dx"` =
Options
`"x"/2 sqrt(1 + "x"^2) + 1/2 log ("x" + sqrt(1 + "x"^2))`+ c
`2/3 (1 + "x"^2)^(3/2) + "c"`
`1/3 (1 + "x"^2)` + c
`("(x)")/sqrt(1 + "x"^2)` + c
Advertisements
Solution
`"x"/2 sqrt(1 + "x"^2) + 1/2 log ("x" + sqrt(1 + "x"^2))`+ c
Explanation:
∵ `int sqrt(a^2 + "x"^2) "dx"` = `x/2 sqrt(a^2 + x^2) + a^2/2 log | x + sqrt(a^2 + x^2)| + c`
∴ I = `x/2 sqrt(1 + x^2) + 1/2 log |x + sqrt(1 + x^2) + c`
APPEARS IN
RELATED QUESTIONS
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
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)`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate: `int "e"^sqrt"x"` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int x^x (1 + logx) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int(log(logx) + 1/(logx)^2)dx` = ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
