Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
पर्याय
`e^x - (1)/(3e^(3x)) + c`
`e^x + (1)/(3e^(3x)) + c`
`e^-x + (1)/(3e^(3x)) + c`
`e^-x - (1)/(3e^(3x)) + c`
Advertisements
उत्तर
`e^x - (1)/(3e^(3x)) + c`
[ Hint : `int (e^(2x) + e^-2x)/e^x*dx`
= `int e^x*dx + int e^(-3x)*dx`
= `e^x + (e^(-3x))/((- 3)) + c`
= `e^x - (1)/(3e^(3x)) + c`].
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`1/(1 - tan x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals:
`int x/(x + 2).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 : `(logx)^n/x`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate `int 1/((2"x" + 3))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int x/(x + 2) "d"x`
`int sin^-1 x`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
`int ("d"x)/(x(x^4 + 1))` = ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
