Advertisements
Advertisements
प्रश्न
The value of `inta^x.e^x dx` equals
पर्याय
`(a^x.log_ea)e^x + c`
`(a^x.e^x)/(log_e(ae)) + c`
`(a^x.e^x)/(log_(ae)e) + c`
`log_e(ae)(ae)^x + c`
उत्तर
`bb((a^x.e^x)/(log_e(ae)) + c)`
APPEARS IN
संबंधित प्रश्न
Integrate : sec3 x w. r. t. x.
Integrate the function in `x^2e^x`.
Integrate the function in x sin-1 x.
Integrate the function in ex (sinx + cosx).
Evaluate the following : `int x tan^-1 x .dx`
Evaluate the following : `int log(logx)/x.dx`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Evaluate the following.
`int "x"^2 "e"^"4x"`dx
Evaluate the following.
`int "x"^3 "e"^("x"^2)`dx
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int 1/x "d"x` = ______ + c
`int logx/(1 + logx)^2 "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
`int tan^-1 sqrt(x) "d"x` is equal to ______.
`int 1/sqrt(x^2 - a^2)dx` = ______.
Solve: `int sqrt(4x^2 + 5)dx`
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
