Advertisements
Advertisements
Question
`int sqrt(x^2 + 2x + 5)` dx = ______________
Options
`(x + 1) sqrt(x^2 + 2x + 5) + log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`
`(x + 2) sqrt(x^2 + 2x + 5) + log [(x + 2) + sqrt(x^2 + 2x + 5)] + "c"`
`(("x" + 2)/2) sqrt(x^2 + 2x + 5) + 1/2 log [(x + 2) + sqrt(x^2 + 2x + 5)] + "c"`
`(("x" + 1)/2) sqrt(x^2 + 2x + 5) + 2 log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`
Advertisements
Solution
`(("x" + 1)/2) sqrt(x^2 + 2x + 5) + 2 log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`
APPEARS IN
RELATED QUESTIONS
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
`int (dx)/(sin^2 x cos^2 x)` equals:
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (3"x"^2 - 5)^2` dx
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
