Advertisements
Advertisements
Question
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Solution
Let I = I
= `int "e"^x (sec x + sec x tan x) "d"x`
Take f(x) = sec x
f‘(x) = sec x tan x
This is of the form of `int "e"^x ["f"(x) + "f'"(x)] "d"x = "e"^x "f"(x) + "c"`
= ex sec x + c
APPEARS IN
RELATED QUESTIONS
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
