Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
विकल्प
`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
Integrate the functions:
sec2(7 – 4x)
Evaluate : `∫1/(3+2sinx+cosx)dx`
Solve:
dy/dx = cos(x + y)
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
`int logx/(log ex)^2*dx` = ______.
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int x^x (1 + logx) "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int(1 - x)^(-2) dx` = ______.
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int x^3"e"^(x^2) "d"x`
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int (logx)^2/x dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
