Advertisements
Advertisements
प्रश्न
Write a value of\[\int a^x e^x \text{ dx }\]
Advertisements
उत्तर
∫ ax . ex dx
= ∫ (ae)x dx
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: `int "e"^sqrt"x"` dx
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int sec^6 x tan x "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int cos^3x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
`int x^3 e^(x^2) dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int(1+x+x^2/(2!))dx`
