how to calculate $\int_C \frac{2xy^2dx-2yx^2dy}{x^2+y^2},$ where $C$ is the ellipse $3x^2 +5y^2 = 1$ taken in the positive direction.
67185
how to calculate $\int_C \frac{2xy^2dx-2yx^2dy}{x^2+y^2}$ using green theorm or directly
103555
Find all positive integral soludions of $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 4$
100817
Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$
120088
How do I calculate a double integral like $\iint_\mathbf{D}e^{\frac{x-y}{x+y}}dx\,dy$?
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
144811
Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
506
Finding $\int x^xdx$
21616
Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $
58947
Integral of $\int\sin^{3}xdx$
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
150809
Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
156485
How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$?
156215
Integral $\int\frac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$
84826
Evaluating $\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx$ using complex analysis
24832
Integrating $\frac{1}{\sqrt{ax^2+bx+c}}$ for $a<0$
140260
Is $\int \frac{1}{2x} \, dx $ equal to $\frac{\ln|2x|}{2}+ C$ or $\frac{\ln|x|}{2}+ C$
120085
Compute $\int \frac{-3}{2x^2-x-1} dx$