Advertisements
Advertisements
प्रश्न
Integrate the function in x sec2 x.
Advertisements
उत्तर
Let `I = int x sec^2 x dx`
Put `u = x, v = sec^2 x`
`therefore int uv dx = u int v dx - int ((du)/dx int v dx) dx`
`= x int sec^2 x dx - int [(d(x))/dx int sec^2 x dx] dx`
`= x tan x - int 1. tan x dx`
`= x tan x + log abs (cos x) + C`
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sin 3x.
`int e^x sec x (1 + tan x) dx` equals:
Find :
`∫(log x)^2 dx`
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
`int (sinx)/(1 + sin x) "d"x`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
`int(logx)^2dx` equals ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`int(1-x)^-2 dx` = ______
Evaluate the following.
`int x^3 e^(x^2) dx`
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int1/(x+sqrt(x)) dx` = ______
`inte^(xloga).e^x dx` is ______
`int(xe^x)/((1+x)^2) dx` = ______
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
