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
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate: `int log ("x"^2 + "x")` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int (cos2x)/(sin^2x) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
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 ______.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
`int x^3 e^(x^2) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
