Antiderivative calculator recommendations

[Coldie]

Does anyone know of a good, preferably flash or html-based antiderivative calculator? I'm on a Mac and can't run any windows executable file.
https://www.symbolab.com/solver/antiderivative-calculator

And if not, would someone please tell me the antiderivative of tan?

[edit]
I'll just give the problem I'm working on. I'm trying to find the integral.

$$\int_{0}^{\pi/4}\frac{1 + \cos^2\theta}{\cos^2\theta}d\theta$$

Subbing in $$\sin^2\theta$$ for $$1 + \cos^2\theta$$, I get $$\int_{0}^{\pi/4}\frac{\sin^2\theta}{\cos^2\theta}d\theta$$ , which I simplified to $$\int_{0}^{\pi/4}\tan\theta d\theta$$

Assuming I'm correct up to this point, all I need is the antiderivative of tangent to complete the problem.

 

[dextercioby]

Does anyone know of a good, preferably flash or html-based antiderivative calculator? I'm on a Mac and can't run any windows executable file.

And if not, would someone please tell me the antiderivative of tan?

Trust me,the best antiderivative calculator will always be the human mind.I've heard that Wolfram's "Mathematica" can make wonders... But of course,it's still human made...

Apply the definition of tangent.Pay attention with the domains of the functions.

Daniel.

 

[Coldie]

Edited the original post with the problem I'm working on. I'm sorry, but it's late and I've been doing this pretty much all day. By definition of tangent, do you mean $$\sin\theta/\cos\theta$$?

 

[dextercioby]

Does anyone know of a good, preferably flash or html-based antiderivative calculator? I'm on a Mac and can't run any windows executable file.

And if not, would someone please tell me the antiderivative of tan?

[edit]
I'll just give the problem I'm working on. I'm trying to find the integral.

$$\int_{0}^{\pi/4}\frac{1 + \cos^2\theta}{\cos^2\theta}d\theta$$

Subbing in $$\sin^2\theta$$ for $$1 + \cos^2\theta$$, I get $$\int_{0}^{\pi/4}\frac{\sin^2\theta}{\cos^2\theta}d\theta$$ , which I simplified to $$\int_{0}^{\pi/4}\tan\theta d\theta$$

Assuming I'm correct up to this point, all I need is the antiderivative of tangent to complete the problem.

Yes,i meant that definition.

Wow,there are a lot of mistakes in what u did up there...First of all,u need to understand that
$$\sin^{2}\theta\neq 1+\cos^{2}\theta$$ (1)

Split you integral into two simpler ones...An antiderivative, often referred to as an indefinite integral, represents the reverse process of finding the original function when you know its derivative. To calculate an antiderivative, you can use integral calculus. Here's how you can find the antiderivative of a function:

1. Identify the function for which you want to find the antiderivative. Let's say it's $f(x)$.

2. Use the power rule for integration. If $f(x)$ is a polynomial, you can apply the power rule:

$$ \int f(x) \, dx = \frac{1}{n+1}x^{n+1} + C $$

Where $n$ is the exponent of the term in $f(x)$, and $C$ is the constant of integration.

3. If $f(x)$ is not a polynomial, you'll need to use more advanced integration techniques. In such cases, you may use integration tables, software, or tools to assist you in finding the antiderivative.

4. Always remember to include the constant of integration, $C$, because when finding an antiderivative, there are often multiple functions that could have the same derivative.

If you're looking for a quick online tool to compute antiderivatives, you can use calculus software or online calculators. There are many websites and software applications that provide this functionality. You simply input the function for which you want to find the antiderivative, and the tool will give you the result, often including the constant of integration.

Keep in mind that some antiderivatives might not have elementary solutions and would require more advanced techniques or computer algebra systems to find their antiderivatives.

 

[Coldie]

Sorry, I was thinking of $$1-\cos^{2}\theta$$. Totally went the wrong way about it.

$$\int_{0}^{\pi/4}\sec^2\theta + 1$$

Antiderivative of which is $$\tan\theta + \theta$$, and the answer is 1 + $$\pi/4$$. Major brain hiccup here. Thanks again!

Antiderivative calculator?