How to show the integral symbol on this site? [duplicate]

Question

On this question: How do I use substitution in integrals? there are examples of what I want. I just want to show integrals on my questions like that. How can I do it?

Answer 1

For basics about MathJax, which is used at this site to typeset math, see editing help or this question.

Specifically for integrals:

You can get integral like this:
$$\int x^2 \, dx = \frac{x^3}3 +C$$ $$\int x^2 \, dx = \frac{x^3}3 +C$$ Notice \, in front of dx - this adds a small space between them, so it looks better.

You can write multiple integrals like this:
$$\iint r(\cos\varphi+\sin\varphi)\,d\varphi\,dr$$ $$\iint r(\cos\varphi+\sin\varphi)\, d\varphi\, dr$$ Writing \iint gives you better spacing than just \int\int. For triple integrals:
$$\iiint 1 \,dx \,dy \,dz$$ $$\iiint 1 \,dx \,dy \,dz.$$

If you want definite integrals, you can add bounds like this:
$$\int_0^1 x^2 \,dx= \frac13$$
$$\int_0^1 \int_0^{2\pi} r \,d\varphi\,dr$$
$$\iint_{x^2+y^2\le 1} x+y \,dx\,dy$$
$$\int_0^1 x^2 \,dx= \frac13\\ \int_0^1 \int_0^{2\pi} r \,d\varphi\,dr\\ \iint_{x^2+y^2\le 1} x+y \,dx\,dy$$ Notice that if the subscript or superscript has more than one symbol, you have to enclose it in {}, e.g. $\int_{-\pi}^\pi$ or $\int_0^{2\pi}$. (Or course, you can use curly brackets even if there is only one symbol, e.g. $\int_{0}^{1}$ works fine; but they are not necessary.) Here is what these examples look like: $\int_{-\pi}^\pi$; $\int_0^{2\pi}$ and $\int_{0}^{1}$.

Another useful thing - if you are using substitution or per partes you might want to indicate what you are doing, e.g. like this:
$$\int \cos x \sin x \,dx = \left| \begin{array}{c} u=\sin x \\ du=\cos x\,dx \end{array} \right| =\int u \,du$$ $$\int \cos x \sin x \,dx = \left| \begin{array}{c} u=\sin x \\ du=\cos x\,dx \end{array} \right| =\int u \,du$$ $$\int x\cos x\, dx = \left| \begin{array}{cc} u=x & v'=\cos x \\ u'=1 & v=\sin x \end{array} \right| = x\sin x - \int \sin x \,dx$$ $$\int x\cos x\, dx = \left| \begin{array}{cc} u=x & v'=\cos x \\ u'=1 & v=\sin x \end{array} \right| = x\sin x - \int \sin x \,dx$$

Integrals are rendered slightly differently in centered formulas (marked by pairs of dollars) and inline mode, compare this:
$$\int_a^b f(x) \,dx,$$ $\int_a^b f(x) \,dx$ and $\int\limits_a^b f(x)\,dx$. $$\int_a^b f(x) \,dx,$$ $\int_a^b f(x) \,dx$ and $\int\limits_a^b f(x)\,dx$.