# Tagged Questions

Question about finding the primitives of a given function, whether or not elementary.

163 views

87 views

62 views

### How to solve $\int \frac{1}{x^2+4x+7} dx$?

How to solve $\int \frac{1}{x^2+4x+7} dx$? I think the first step is to write it in the following form: $$\int \frac{1}{(x+2)^2+3} dx$$
46 views

### solution of the ODE $u du =ydx+xdy$

In this case $u=u(x,y)$. When I saw this I just went on to taking iindefinite integral both sides yielding $u^2=4xy+K$. Yet, the book I am using now got $udu=d(xy)$, which yields $u^2=2xy+K$. I'm I ...
31 views

### Find the primitive functions in given intervals [on hold]

I can easy compute the indefinite integral, but I have a problem with understanding the condition and I don't know what to do next - I don't know how to find a primitive function in a given interval. ...
69 views

67 views

48 views

### Why $C=1$ in indefinite integral $\int{\sin x\,\mathrm{d}x}$

I am reading Introduction to Calculus and Analysis by Richard Courant. In Section 3.15, g.The Dirichlet Integral, it said $\int{\sin x \,\mathrm{d}x}=1-\cos x$,why $C=1$ here?
93 views

### 2 Weird questions

Seems like I'm full of weird mathematical questions! Last time I made a question about imaginary numbers. This time I have 2 seemingly unrelated questions. But nevertheless it's always good (and fun)...
77 views

### Finding $\int \frac{\mathrm{d}x}{1 + \frac{2}{x} - x}$

I want to solve: $$\int\frac{1}{1+\frac{2}{x}-x} \mathrm{d}x$$ I don't know how to start, maybe I should use partial fraction?
What is the real integral of the function $$f(x) =\frac{1-x^2}{(1 + x^2)^2}$$? Is it $F_1(x) = \frac{x}{1 + x^2} + C$ or $F_2(x) = \arctan x + C$ ? The brochure I was reading gave the first result ...