Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Advertisements
उत्तर
Let I = `int "e"^x (tan x + log sec x) "d"x`
Take f(x) = log sec x
f'(x) = `1/sec x sec x tan x`
f'(x) = tan x
`[int"e"^x ["f"(x) + "f"(x)] "d"x = "e"^x"f"(x) + "c"]`
∴ I = ex log |sec x| + c
APPEARS IN
संबंधित प्रश्न
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
