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The substitution u = tan(x) gives integral (sec^2(x).tan(x)) dx = integral (x) du = 1/2.u^2 + C = 1/2.tan^2(x) + C. The substitution u=sec(x) gives integral (sec^2(x).tan(x)) dx = integral (x) du = 1/2.u^2 + C = 1/2. sec^2(x) + C. Can both in...
Evaluate the integral. \int \frac{sin(tanx)}{cos^2x} dx Evaluate the integral of (9x-2)^(-3) dx. Evaluate the integral from 2 to 4 of x*sqrt(x - 2) dx. Evaluate the integral: int_{0}^{3} mid x-2 mid dx. Evaluate the integral of 3x^2 cos(3x) dx. ...
1Use integration by parts to find the integral of the following functions with respect to x:Hint: In (7) write as .In (9) write as .(1)(2)(3)(4)(5)(6)(7)(8)(9) 2Use integration by parts to find the integral of:[Hint: In (7) write as and in (9) write as .](1...
Find an anti derivative (or integral) of the following functions by t... 01:40 Find the integralint(2x^2+e^x)dx 00:58 Find the integralint(a x^2+b x+c)dx 01:43 Find the integralintsecx(secx+tanx)dx 00:50 Find the integralint(sec^2x)/(cose c^2x)dx 01:12 Find the integra...
59. [T] y=tanxy=tanx over the interval [0,π4][0,π4]; the exact solution is 2ln(2)π2ln(2)π.60. [T] y=x+1√4−x2y=x+14−x2 over the interval [−1,1][−1,1]; the exact solution is π6π6. Show Solution ...
Evaluate the integral. Integral from 2*sqrt(2) to 4 of 1/(t^3 sqrt(t^2 - 4)) dt. Evaluate the integral from 0 to 3/2 of 1/(sqrt(9 - x^2)) dx. Evaluate the integral. xsecxtanx Evaluate the integral. \int_{0}^{1}\frac{\ln x}{\sqrt{xdx Evaluate integral of \...
Since, it should not be difficult to prove fromandthat the-regularization ofequalsas wanted, for instance by computingfor any: Indeed the substitution in and the integral representation for the function complete the proof. Takingwhereis the [Lambertfunction][1] andis the [Polylogarithm function][...
Evaluate the integral∫14(x2−5x+7)dx Fundamental Theorem of Calculus: Assume that the functionf(x)is continuous on the interval[a,b]andF(x)pertains to the antiderivative off(x). Then, the following equation is true according to the fundamental theorem of calculus: ...
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