The antiderivative of sin 2 x is x/ 2 - (sinx cosx) / 2. Explore math program.

Sep 17, 2015 · How do I evaluate the indefinite integral #int(tan^2(x)+tan^4(x))^2dx# ? How do I evaluate the indefinite integral #intx*sin(x)*tan(x)dx# ? See all questions in Integrals of Trigonometric Functions

Feb 20, 2015 · Because $$\int_0^{\pi}\sin(x)\,\mathrm{d}x=2,$$ then $$\int_0^{16\pi}|\sin(x)|\,\mathrm{d}x=32.$$ And Wolfram Alpha agrees to this, but when I ask for the indefinite ...

∫2x cos (x 2) dx = ∫cos u du = sin u + C = sin (x 2) + C. Antiderivative Product Rule. The antiderivative product rule is also commonly called the integration by parts method of integration. It is one of the important antiderivative rules and is used when the antidifferentiation of the product of functions is to be determined.

Feb 21, 2022 · Why isn't the antiderivative of $\sin(2x) = \sin^2(x)$? I notice that derivative of $\sin^2(x) = 2\sin(x)\cos(x)$ which is also equal to $\sin(2x)$. Now, according to the fundamental theorem of calculus, integration and differentiation are inverse processes, so the integration of $\sin(2x)$ should be $\sin^2(x) + C$ which I think is not true.

Jun 6, 2015 · How do I evaluate the indefinite integral #int(tan^2(x)+tan^4(x))^2dx# ? How do I evaluate the indefinite integral #intx*sin(x)*tan(x)dx# ? See all questions in Integrals of Trigonometric Functions

1/4x^2-1/4xsin2x+1/8cos2x I = intxsin^2xdx cos2x= cos^2-sin^2x , rArr sin^2x= (1-cos2x)/2 I = intxsin^2xdx = int(x(1-cos2x))/2dx I = 1/2intxdx- 1/2intxcos2xdx Let evaluate the second part first. Let u = 2x rArr du = 2dx and perform integration by parts 1/2intxcos2xdx = 1/8 intucosudu= 1/8 (usinu-intsinudu) =1/8 (usinu+cosu) I = 1/4x^2-1/8(2xsin2x+cos2x) I= 1/4x^2-1/4xsin2x+1/8cos2x

$\begingroup$ It's correct to say that the integral of $\sin^2x\cos x$ is $\frac13\sin^3x$. But that doesn't mean that the integral of $\sin^2x$ is $\frac13\sin^3x/\cos x$. That reasoning would only be valid if $\cos x$ were constant, which it's not. $\endgroup$ –

The antiderivatives of a function x could be x 2 /2 + 2, x 2 /2 - 32, x 2 /2 + 19.2, and so on (try to differentiate each of these and find the result to be x). Thus, it can be said that antiderivatives of a function will differ by a constant .

Sep 2, 2018 · $$\mathrm{Si}(x) := \int_{0}^{x} \frac{\sin(x')}{x'}\ dx'$$.. The above theorem, suffices to make this definition correct. In fact the above theorem even guarantees this has an antiderivative as well, so it's not restricted to just "elementary" functions alone as the above function is not elementary, as you already mentioned. (In fact we can ...