Question

Is there a general formula for $\int{\big(\frac {\arctan x}{x^2+1} \big )}^{\frac1k}dx$ , with $k$ is positive integer?

score 65 · Answer 1 · 2026-04-15 15:07:07

65

Views

Is there a general formula for $\int{\big(\frac {\arctan x}{x^2+1} \big )}^{\frac1k}dx$ , with $k$ is positive integer?

Published on 15 Apr 2026 - 15:07

score 274 · Answer 2 · 2026-04-15 21:01:01

274

Views

Simplify $y = \frac{1-2\exp(-x)\cos(x)+\exp(-2x)}{1+2\exp(-x)\sin(x)-\exp(-2x)}$

Published on 15 Apr 2026 - 21:01

score 166 · Answer 3 · 2026-04-16 06:27:34

166

Views

$ \cos (x+a) + \cos( X+b) + \cos( X+c ) = 0$ find possible values of $(c-a) $

Published on 16 Apr 2026 - 6:27

score 301 · Answer 4 · 2026-04-16 21:16:38

301

Views

Solution of Trig equation $\sin x+2\cos x=1+\sqrt{3}\cos x$

Published on 16 Apr 2026 - 21:16

score 268 · Answer 5 · 2026-04-15 07:48:33

268

Views

Prove that, $\cos x\ge1-{2x\over\pi}\ \forall x\in[0,{\pi\over2}]$

Published on 15 Apr 2026 - 7:48

score 106 · Answer 6 · 2026-04-16 11:59:26

106

Views

$\int \frac{dx}{\sin^3{x}}$ possible with universal substitution?

Published on 16 Apr 2026 - 11:59

score 158 · Answer 7 · 2026-04-15 01:17:43

158

Views

Show the inequality $\lvert \sin(z)\rvert > \frac{2}{\pi}$ for $z$ on the circle of radius $(n+1/2) \pi$.

Published on 15 Apr 2026 - 1:17

score 107 · Answer 8 · 2026-04-14 12:22:50

107

Views

What is $\tan^{-1}(x) - \tan^{-1}\big(\frac{1}{x}\big)$?

Published on 14 Apr 2026 - 12:22

score 58 · Answer 9 · 2026-04-12 03:26:31

58

Views

Calculating Arc Hyperbolic CoTangent faster than using a standard power series

Published on 12 Apr 2026 - 3:26

score 136 · Answer 10 · 2026-04-15 15:23:44

136

Views

Limit of $\frac{\sin\frac 1 x}{\sin\frac 1 x}$ as $x$ goes to zero

Published on 15 Apr 2026 - 15:23

score 60 · Answer 11 · 2026-04-16 04:05:34

60

Views

Hints for solving $\tan(x) = 1 - 2\sin(x)$ for the domain of $[0, \pi/4]$

Published on 16 Apr 2026 - 4:05

score 63 · Answer 12 · 2026-04-14 15:22:30

63

Views

Trigonometry equation that includes two sin and a cos

Published on 14 Apr 2026 - 15:22

score 31 · Answer 13 · 2026-04-11 21:17:45

31

Views

Understanding an argument given in my textbook about a second order linear ODE with Dirichlet boundary conditions

Published on 11 Apr 2026 - 21:17

score 410 · Answer 14 · 2026-04-11 09:35:58

410

Views

Simplify trigonometric expression using trigonometric identities

Published on 11 Apr 2026 - 9:35

score 84 · Answer 15 · 2026-04-13 04:25:57

84

Views

Reason for Z-axis orientation in torus knots

Published on 13 Apr 2026 - 4:25

List Question

Is there a general formula for $\int{\big(\frac {\arctan x}{x^2+1} \big )}^{\frac1k}dx$ , with $k$ is positive integer?

Simplify $y = \frac{1-2\exp(-x)\cos(x)+\exp(-2x)}{1+2\exp(-x)\sin(x)-\exp(-2x)}$

$ \cos (x+a) + \cos( X+b) + \cos( X+c ) = 0$ find possible values of $(c-a) $

Solution of Trig equation $\sin x+2\cos x=1+\sqrt{3}\cos x$

Prove that, $\cos x\ge1-{2x\over\pi}\ \forall x\in[0,{\pi\over2}]$

$\int \frac{dx}{\sin^3{x}}$ possible with universal substitution?

Show the inequality $\lvert \sin(z)\rvert > \frac{2}{\pi}$ for $z$ on the circle of radius $(n+1/2) \pi$.

What is $\tan^{-1}(x) - \tan^{-1}\big(\frac{1}{x}\big)$?

Calculating Arc Hyperbolic CoTangent faster than using a standard power series

Limit of $\frac{\sin\frac 1 x}{\sin\frac 1 x}$ as $x$ goes to zero

Hints for solving $\tan(x) = 1 - 2\sin(x)$ for the domain of $[0, \pi/4]$

Trigonometry equation that includes two sin and a cos

Understanding an argument given in my textbook about a second order linear ODE with Dirichlet boundary conditions

Simplify trigonometric expression using trigonometric identities

Reason for Z-axis orientation in torus knots

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