Advertisements
Advertisements
Question
`int e^x sec x (1 + tan x) dx` equals:
Options
ex cos x + C
ex sec x + C
ex sin x + C
ex tan x + C
Advertisements
Solution
ex sec x + C
Explanation:
Let `I = int e^x sec x (1 + tan x) dx`
`= int e^x (sec x + sec x tan x) dx`
` = int (sec x) e^x dx + int e^x sec x tan x dx`
`= I_1 + int e^x sec x tan x` .... (1)
`I_1 = int (sec x)e^x dx`
`I_1 = (sec x) int e^x dx - int (sec x tan x int e^x dx) dx`
`= (sec x) e^x - int e^x sec x tan x dx`
Putting this value in equation (1),
`I = I_1 + int e^x sec x tan x dx`
`= (sec x) e^x - int e^x sec x tan x dx + int e^x sec x tan x dx + C`
`= e^x sec x + C`
APPEARS IN
RELATED QUESTIONS
Integrate the function in x log x.
Integrate the function in x sin−1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in e2x sin x.
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int log(logx)/x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Find `int_0^1 x(tan^-1x) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
`int(logx)^2dx` equals ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
`inte^(xloga).e^x dx` is ______
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
