0
let u = x du=dx
let dv= e^x v=e^x
∫ xe^(x)dx =
xe^x - ∫ e^(x)dx
= xe^x - e^x
= e^x ( x-1 ) + c
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∙ 12y ago
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What is the indefinite integral?
An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number. The general form of a definite integral is: ∫ba f(x) dx. The general form of an indefinite integral is: ∫ f(x) dx. An example of a definite integral is: ∫20 x2 dx. An example of an indefinite integral is: ∫ x2 dx In the definite case, the answer is 23/3 - 03/3 = 8/3. In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.
What is the integral of cosine?
∫ cos(x) dx = -sin(x) + C
What is the antiderivative of x to the 1?
By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2
What is the integral of x diveded by x minus one?
integral x/(x-1) .dx = x - ln(x-1) + c where ln = natural logarithm and c = constant of integration alternatively if you meant: integral x/x - 1 .dx = c
What is the integral of a constant multiplied by a function of x with respect to x?
∫ af(x) dx = a ∫ f(x) dx
What are the main guidelines of FERA?
xex dx
Integral of 1 divided by sinx cosx?
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C
Integral of -3 dx?
-3x
What is the indefinite integral of 3sinx-5cosx?
8
Integral of x cosx dx?
The integral of x cos(x) dx is cos(x) + x sin(x) + C
What is the indefinite integral?
An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number. The general form of a definite integral is: ∫ba f(x) dx. The general form of an indefinite integral is: ∫ f(x) dx. An example of a definite integral is: ∫20 x2 dx. An example of an indefinite integral is: ∫ x2 dx In the definite case, the answer is 23/3 - 03/3 = 8/3. In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.
Integral formula of a raised to x?
integral (a^x) dx = (a^x) / ln(a)
What is the integral of -3dx?
∫(-3)dx = -3x + C
How do you integrate 2x over 2x-2?
Integral of 2x dx /(2x-2) Let 2x=u 2 dx = du dx = (1/2) du Integral of 2x dx /(2x-2) = Integral of (1/2) u du / (u-2) = Integral of 1/2 [ (u-2+2) / (u-2)] dx = Integral of 1/2 [ 1+ 2/(u-2)] dx = u/2 + (1/2) 2 ln(u-2) + C = u/2 + ln(u-2) + C = (2x/2) + ln(2x-2) + C = x + ln(2x-2) + C
What is the integral for sin3x?
S sin3X dx =-1/3 cos3X
What is the integral of cosine?
∫ cos(x) dx = -sin(x) + C
Does f-gx equals g-fx?
Yes, the integral of gx dx is g integral x dx. In this case, g is unrelated to x, so it can be treated as constant and pulled outside of the integration.
