I wasn't entirely sure what you meant, but if the problem was to find the integral of [sec(2x)-cos(x)+x^2]dx, then in order to get the answer you must follow a couple of steps:
The integral of sec(2x) is -(cos(2x)/2)
The integral of cos(x) is sin(x)
The integral of x^2 is
-(cos(2x)/2) - sin(x) + (x^3)/3
arctan(x)
8
I will assume that this is sopposed to be integrated with respect to x. To make this problem easier, imagine that the integrand is x raised to the negative 3. The integral is 1/(-2x-2) plus some constant c.
Do you mean the Convolution Integral?
The integral of -x2 is -1/3 x3 .
What is the number of integral solution to x plus y plus z equals 100?
The integral of 1 + x2 is x + 1/3 x3 + C.
Integral of 1 is x Integral of tan(2x) = Integral of [sin(2x)/cos(2x)] =-ln (cos(2x)) /2 Integral of tan^2 (2x) = Integral of sec^2(2x)-1 = tan(2x)/2 - x Combining all, Integral of 1 plus tan(2x) plus tan squared 2x is x-ln(cos(2x))/2 +tan(2x)/2 - x + C = -ln (cos(2x))/2 + tan(2x)/2 + C
it is not possible to get the Integral of cos2x log cosx-sinx coax plus since there are no symbols given in the equation.
Integral (14+x^4) dx = 14x + x^5/5 + C
3
arctan(x)
If x has the power 2 then you want the integral of x2, I think. When you integrate this you get : x3/3 , plus a constant.
x3 /12 + 16x + c
If you mean integral[(2x^2 +4x -3)(x+2)], then multiply them out to get: Integral[2x^3+8x^2+5x-6]. This is then easy to solve and is = 2/4x^4+8/3x^3+5/2x^2-6x +c
x/(x+1) = 1 - 1/(x + 1), so the antiderivative (or indefinite integral) is x + ln |x + 1| + C,
Without specifying the limits of integration, the integral will always include an arbitrary constant, and you'll never get a numerical value for it. So the statement is untrue on its face, hence unprovable. We'll have a look at the trig later.