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 solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
cot2x + tan2x
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 :
sin5x cos3x
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:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
