Linked Questions

5
votes
4answers
428 views

Evaluate $\int\frac{\cos x}{\sin x + \cos x}\,\text{d}x$. [duplicate]

I'm trying to figure out how to take this indefinite integral: $$ \int\frac{\cos x}{\sin x + \cos x}\,\text{d}x.$$ I tried simplifying and rearranging it, and this is the best I got: $$\int\frac{1}{\...
4
votes
5answers
396 views

What is $\int\frac{dx}{x+\sqrt{1-x^2}}$? [duplicate]

Possible Duplicate: Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ $$\int\frac{dx}{x+\sqrt{1-x^2}}$$ I used $x = \sin(a),\ dx = \cos (a)\,da$. However, I am getting suck after that. ...
0
votes
3answers
122 views

How to calculate $\int_{0}^{\pi/4} \frac{\sin x}{\sin x + \cos x} \, dx$ [duplicate]

Can somebody give mi idea, how to solve this integral? $$\int_{0}^{\pi/4} \frac{\sin x}{\sin x + \cos x} \, dx$$
-1
votes
1answer
62 views

Not able to integrate $ \int \frac{\sin x}{\sin x + \cos x} \ dx $ ?? [duplicate]

$$ \int \frac{\sin x}{\sin x + \cos x} \ dx $$ So what I thought of doing was converting $\sin x$ and $\cos x$ into $\tan\frac{x}{2}$ But it got converted into non integrable form Any other ...
3
votes
7answers
266 views

Is there another simple way to solve this integral $I=\int\frac{\sin{x}}{\sin{x}+\cos{x}}dx$?

The integral I want to find is$$I=\int\frac{\sin{x}}{\sin{x}+\cos{x}}dx$$ The way I learnt is to introduce$$J=\int\frac{\cos{x}}{\sin{x}+\cos{x}}dx$$ Then $J+I=x+C_1$ and $J-I=\ln|\sin{x}+\cos{x}|+C_2$...
4
votes
3answers
3k views

Integrating $ \int \frac{1}{1-\tan(x)}dx $

$$ \int \frac{dx}{1-\tan(x)} $$ Please help me to solve this problem as I'm trying this since last 1 day...
3
votes
4answers
222 views

Different ways of evaluating $\int_{0}^{\pi/2}\frac{\cos(x)}{\sin(x)+\cos(x)}dx$

My friend showed me this integral (and a neat way he evaluated it) and I am interested in seeing a few ways of evaluating it, especially if they are "often" used tricks. I can't quite recall his way,...
0
votes
5answers
157 views

Evaluation of $\int_{0}^{1} \frac{1}{x+\sqrt{1-x^2}} \space dx$

Evaluate $$\int_{0}^{1} \frac{1}{x+\sqrt{1-x^2}} \space dx$$ My main concern is finding the indefinite integral as once i have that the rest is fairly straight forward. Please give a detailed answer ...
1
vote
3answers
208 views

Integral with goniometric functions $\int(1+\cos^2x-\sin^2x)dx$

I am solving this example: Transcription: \begin{align} &\int(1+\cos^2x-\sin^2x)dx=\int(1+1-\sin^2x-\sin^2x)dx=\int(2-2\sin^2x)dx=\\ &\quad=\int2(1-\sin^2x)dx=2\int(1-\sin^2x)dx=2\left[\...
0
votes
3answers
100 views

How do solve $\int\frac{2\sin(x)+3\cos(x)}{3\sin(x)+2\cos(x)}dx$? [duplicate]

How do I solve this integral? Should I use some kind of an integral substitution?
0
votes
2answers
95 views

Evaluation of $\int\frac{x^3+3x+2}{(x^2+1)^2\cdot (x+1)}dx$

Evaluation of $\displaystyle \int\frac{x^3+3x+2}{(x^2+1)^2\cdot (x+1)}\;,$ Can we solve it without Using Partial fraction. $\bf{My\; Try::}$ Let $\displaystyle I = \int\frac{x^3+x+2x+2}{(x^2+1)^2\...
1
vote
0answers
95 views

Integration Tips and Tricks [duplicate]

Im looking for Tips and Tricks for integration. I know all the basic techniques (substitution, completing the square, parts etc.) I'm mainly interested in dealing with logs in the denominator and ...
1
vote
0answers
50 views

$\int_0^x \frac{\cos(t)}{\sin(t)+\cos(t)} dt$ and $\int_0^x \frac{\sin(t)}{\sin(t)+\cos(t)} dt$

Let $x\in[0,\pi/2]$, $I(x)=\int_0^x \frac{\cos(t)}{\sin(t)+\cos(t)} dt$ and $J(x)=\int_0^x \frac{\sin(t)}{\sin(t)+\cos(t)} dt$ . The aim of the exercise is to calculate $I(x)$ and $J(x)$. Fisrt of ...