Advertisements
Advertisements
प्रश्न
Write a value of\[\int a^x e^x \text{ dx }\]
उत्तर
∫ ax . ex dx
= ∫ (ae)x dx
APPEARS IN
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int \log_e x\ dx\].
Write a value of
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3)dx`
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).