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(e^x)^8 can be written as e^(8*x), so the integral of e^(8*x) = (e^(8*x))/8 or e8x/ 8, then of course you have to add a constant, C.
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What is the antiderivative of e raised to the one tenth x?
The integral would be 10e(1/10)x+c
Integral of e to the power of -x?
integral of e to the power -x is -e to the power -x
What is the integral of e raised to the cube root of x?
A primitive to e^(x^(1/3)) is (e^(x^(1/3)))*(6-6x^(1/3)+3x^(2/3))
What is the integral of e raised to x cubed?
(ex)3=e3x, so int[(ex)3dx]=int[e3xdx]=e3x/3 the integral ex^3 involves a complex function useful only to integrations such as this known as the exponential integral, or En(x). The integral is:-(1/3)x*E2/3(-x3). To solve this integral, and for more information on the exponential integral, go to http://integrals.wolfram.com/index.jsp?expr=e^(x^3)&random=false
What is the integral of sin x times The exponential of x Times Square x?
Take the integral: integral e^x x^2 sin(x) dx For the integrand e^x x^2 sin(x), integrate by parts, integral f dg = f g- integral g df, where f = x^2, dg = e^x sin(x) dx, df = 2 x dx, g = 1/2 e^x (sin(x)-cos(x)): = 1/2 e^x x^2 sin(x)-1/2 (e^x x^2 cos(x))- integral e^x x (sin(x)-cos(x)) dx Expanding the integrand e^x x (sin(x)-cos(x)) gives e^x x sin(x)-e^x x cos(x): = 1/2 e^x x^2 sin(x)-1/2 (e^x x^2 cos(x))- integral (e^x x sin(x)-e^x x cos(x)) dx Integrate the sum term by term and factor out constants: = 1/2 e^x x^2 sin(x)-1/2 (e^x x^2 cos(x))- integral e^x x sin(x) dx+ integral e^x x cos(x) dx For the integrand e^x x sin(x), integrate by parts, integral f dg = f g- integral g df, where f = x, dg = e^x sin(x) dx, df = dx, g = 1/2 e^x (sin(x)-cos(x)): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)+1/2 e^x x cos(x)+ integral e^x x cos(x) dx+1/2 integral e^x (sin(x)-cos(x)) dx Expanding the integrand e^x (sin(x)-cos(x)) gives e^x sin(x)-e^x cos(x): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)+1/2 e^x x cos(x)+ integral e^x x cos(x) dx+1/2 integral (e^x sin(x)-e^x cos(x)) dx Integrate the sum term by term and factor out constants: = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)+1/2 e^x x cos(x)+1/2 integral e^x sin(x) dx-1/2 integral e^x cos(x) dx+ integral e^x x cos(x) dx For the integrand e^x cos(x), use the formula integral exp(alpha x) cos(beta x) dx = (exp(alpha x) (alpha cos(beta x)+beta sin(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/4 e^x sin(x)-1/2 e^x x sin(x)-1/4 (e^x cos(x))+1/2 e^x x cos(x)+1/2 integral e^x sin(x) dx+ integral e^x x cos(x) dx For the integrand e^x sin(x), use the formula integral exp(alpha x) sin(beta x) dx = (exp(alpha x) (alpha sin(beta x)-beta cos(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)-1/2 (e^x cos(x))+1/2 e^x x cos(x)+ integral e^x x cos(x) dx For the integrand e^x x cos(x), integrate by parts, integral f dg = f g- integral g df, where f = x, dg = e^x cos(x) dx, df = dx, g = 1/2 e^x (sin(x)+cos(x)): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)+e^x x cos(x)-1/2 e^x cos(x)-1/2 integral e^x (sin(x)+cos(x)) dx Expanding the integrand e^x (sin(x)+cos(x)) gives e^x sin(x)+e^x cos(x): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)+e^x x cos(x)-1/2 e^x cos(x)-1/2 integral (e^x sin(x)+e^x cos(x)) dx Integrate the sum term by term: = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)+e^x x cos(x)-1/2 e^x cos(x)-1/2 integral e^x sin(x) dx-1/2 integral e^x cos(x) dx For the integrand e^x cos(x), use the formula integral exp(alpha x) cos(beta x) dx = (exp(alpha x) (alpha cos(beta x)+beta sin(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/4 e^x sin(x)+e^x x cos(x)+-3/4 e^x cos(x)-1/2 integral e^x sin(x) dx For the integrand e^x sin(x), use the formula integral exp(alpha x) sin(beta x) dx = (exp(alpha x) (alpha sin(beta x)-beta cos(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x sin(x)+e^x x cos(x)-1/2 e^x cos(x)+constant Which is equal to: Answer: | | = 1/2 e^x ((x^2-1) sin(x)-(x-1)^2 cos(x))+constant
What is the integral of e raised to x squared?
maths signs
Integral formula of a raised to x?
integral (a^x) dx = (a^x) / ln(a)
What is the antiderivative of e raised to the one tenth x?
The integral would be 10e(1/10)x+c
Integral of e to the power of -x?
integral of e to the power -x is -e to the power -x
What is the integral of e raised to the square root of x?
better place to ask would be yahoo answers
What is the integral of e raised to the square root of x divided by the square root of x?
replace square root o x with t.
What is the integral of e raised to the cube root of x?
A primitive to e^(x^(1/3)) is (e^(x^(1/3)))*(6-6x^(1/3)+3x^(2/3))
Integrate e raised to power x raised to power 2?
This integral cannot be performed analytically. Ony when the integral is taken from 0 to infinity can it be computed by squaring the integral and applying a change of variable (switching to polar coordinates). if desired I could show how to do this.
What is the integral of e raised to x cubed?
(ex)3=e3x, so int[(ex)3dx]=int[e3xdx]=e3x/3 the integral ex^3 involves a complex function useful only to integrations such as this known as the exponential integral, or En(x). The integral is:-(1/3)x*E2/3(-x3). To solve this integral, and for more information on the exponential integral, go to http://integrals.wolfram.com/index.jsp?expr=e^(x^3)&random=false
What is the antiderivative of e to the x plus 17?
I'm not sure if you mean e^x + 17 or e^(x+17) so we'll do both. First, the integral of e^x + 17 because these terms are being added you can integrate them separately: integral((e^x)dx) + integral(17dx) integral of e^x is just e^x + C Integral of 17 is 17x + C, so we get: e^x + 17x + C Second, the integral of e^(x+17) we know how to integrate the form e^u, so just do a u substitution u=x+17 du=dx so we get integral((e^u)du)=e^u + C resubstitute for u and get e^(x+17) + C
Integral of 3 raised to x?
The integral of 3x is ln(3)*3x. Take the natural log of the base and multiply it by the base raised to the power.
What is the integral of the e?
x=1
