Advertisements
Advertisements
Question
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Advertisements
Solution
I = `int "e"^x ((2 + sin 2x)/(1 + cos 2x)) "d"x`
I = `int "e"^x ((2 + 2 sin x cos x)/(2 cos^2 x)) "d"x`
I = `int "e"^x ((2(1 + sin x cos x))/(2 cos^2x)) "d"x`
I = `int "e"^x ((1 + sin x cos x)/(cos^2x)) "d"x`
I = `int "e"^x [1/(cos^2x) + (sin x cos x)/(cos^2x)] "d"x`
I = `int "e"^x [sec^2x + sinx/cosx] "d"x`
I = `int "e"^x [sec^2x + tan x] "d"x`
I = `int "e"^x [tan x + sec^2x] "d"x`
Take f(x) = tan x
f'(x) = sec2 x
`[int "e"^x ["f"(x) + "f"(x)] "d"x = "e"^x "f"(x) + "c"]`
I = ex tan x + c
APPEARS IN
RELATED QUESTIONS
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
