Advertisements
Advertisements
प्रश्न
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Advertisements
उत्तर
Let `I = int (2 + sin 2x)/(1 + cos 2x) e^x dx`
`int (2 + 2 sin x cos x)/(1 + 2 cos^2 x - 1)e^x dx`
`= int (2 (1 + sin x cos x))/(2 cos^2 x) e^x dx`
`= int (sec^2 x * e^x + tan * e^x) dx`
`= int e^x (sec^2 x + tan x) dx`
Putting ex tan x = t
(ex sec2 x + tan x · ex)dx = dt
Hence, I = `int 1 * dt`
= t + C = ex tan x + C
APPEARS IN
संबंधित प्रश्न
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
Find an anti derivative (or integral) of the following function by the method of inspection.
sin 2x
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/sqrt(9x - 4x^2)` equal
`int (xdx)/((x - 1)(x - 2))` equals
`int (dx)/(x(x^2 + 1))` equals
`int e^x sec x(1 + tanx) dx` equals
What is anti derivative of `e^(2x)`
`d/(dx)x^(logx)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
