Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
उत्तर
`int "e"^(x log "a") "e"^x = int "e"^(log "a"^x) * "e"^x * "d"x`
= `int "a"^x "e"^x * "d"x`
= `int ("ae")^x * "d"x`
`[int "a"^x * "d"x = "a"^x/log"a" + "c"]`
= `("ae")^x/(log("ae")) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/(9x^2 - 4)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
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 secx/sqrt(cos2x) "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 x "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
