User user8277998

9 votes

Accepted

Evaluate: $\int \frac {\sec (x)}{\sec (x)+\tan (x)} dx$

answered Jan 24, 2018 at 1:13

7 votes

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Find limit of trigonometric function

answered Sep 25, 2017 at 18:42

7 votes

How to calculate $\lim_{x\to0} \frac{\ln(1+x)+\ln(1-x)}{x^2}$?

answered Nov 1, 2017 at 13:46

7 votes

Find the limit of $\lim_{x\to0}{\frac{\ln(1+e^x)-\ln2}{x}}$ without L'Hospital's rule

answered Dec 21, 2017 at 16:30

6 votes

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Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

answered Sep 23, 2017 at 16:55

5 votes

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How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?

answered Jul 31, 2017 at 8:19

5 votes

Is $\frac{200!}{(10!)^{20} \cdot 19!}$ an integer or not?

answered Aug 15, 2017 at 8:17

5 votes

Suppose $x$ and $y$ are real numbers and $x^2+9y^2-4x+6y+4=0$. Then find the maximum value of $\left(\frac{4x-9y}{2}\right)$

answered Oct 14, 2017 at 19:36

5 votes

How to calculate this hard integral $\int_0^{\infty} \frac{\arctan(x)\sqrt{\sqrt{1+x^2}-1}}{x\sqrt{1+x^2}}\,dx$?

answered Dec 8, 2017 at 19:46

5 votes

Solving $\int\limits_{-\infty}^\infty \frac{1}{x^8+1}dx$ through Glasser's Master Theorem

answered Dec 19, 2018 at 13:03

4 votes

Calculating the limit $\lim\limits_{x \to 0^+} \frac{\sqrt{\sin x}-\sin\sqrt{ x}}{x\sqrt{x}}$

answered Sep 19, 2017 at 9:12

3 votes

Find real solutions in $x$,$y$ for the system $\sqrt{x-y}+\sqrt{x+y}=a$ and $\sqrt{x^2+y^2}-\sqrt{x^2-y^2}=a^2.$

answered Nov 29, 2017 at 11:53

3 votes

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Closed form of $I(t) = \int_0^{\pi/2}\frac{\cos xdx}{\sqrt{\sin^2 x+ t\cos^2 x}}$

answered Dec 5, 2017 at 21:15

3 votes

Integrate $\int \frac{\sin x \cos x}{\sin^4x + \cos^4x} \,dx$

answered Dec 13, 2017 at 2:42

2 votes

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Inner product on a complex field defined by norms

answered Dec 14, 2017 at 19:00

2 votes

Accepted

How to proof: $\cos(10°)\cos(30°)\cos(50°)*\cos(70°)=\frac{3}{16}$

answered Dec 16, 2017 at 18:25

2 votes

Limit of $\lim_{n\to\infty}n\cdot \sqrt[n]{\sin\left(\frac{1}{1}\right)\cdot \sin\left(\frac{1}{2}\right)\cdots\sin\left(\frac{1}{n}\right)}$

answered Dec 11, 2017 at 13:21

2 votes

How to compute $\lim_{x\to 0}\frac{\sin(x^2+x)-x}{x^2}$ without L'Hospital's Rule or series?

answered Oct 15, 2017 at 9:06

2 votes

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Calculate $\lim_{x \to 0} (\cot^3(x)·x·(\ln(1+3x)-3x))$

answered Dec 19, 2017 at 23:01

2 votes

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How does the first equation transform to the second one?

answered Dec 3, 2017 at 18:07

2 votes

Area of ellipse which is not in standard form

answered Sep 30, 2017 at 11:43

2 votes

Accepted

Factorising 4th degree polynomial

answered Oct 11, 2017 at 19:00

2 votes

Find the limit of $\lim\limits_{x\to0^+}\frac{1}{e} \frac{e- e^ \frac{\ln (1+x)}{x}}{x}$ as $x$

answered Feb 1, 2018 at 15:55

1 vote

How to solve $\int \cot^3 x\,dx$?

answered Feb 1, 2018 at 16:11

1 vote

What is $\int \frac{ \sqrt{(a^2 - x^2)}}{x^2}$?

answered Feb 1, 2018 at 20:51

1 vote

Prove that: $\tan (2\tan^{-1} (x))=2\tan (\tan^{-1} (x)+\tan^{-1} (x^3))$

answered Jan 27, 2018 at 15:28

1 vote

Singular Conics and Intersection of Line with a Conic

answered Feb 6, 2019 at 17:09

1 vote

Evaluate $\int \frac{\cos 2x \: dx}{3 \sin x+4 \cos x}$

answered Sep 3, 2017 at 18:08

1 vote

A tough limit problem involving $1/(\sin x - \sin a)$ and its generalization

answered Jan 24, 2018 at 15:39

1 vote

Linear Algebra- Systems of Linear Equations

answered Nov 8, 2017 at 17:05

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45 Answers

Evaluate: $\int \frac {\sec (x)}{\sec (x)+\tan (x)} dx$

Find limit of trigonometric function

How to calculate $\lim_{x\to0} \frac{\ln(1+x)+\ln(1-x)}{x^2}$?

Find the limit of $\lim_{x\to0}{\frac{\ln(1+e^x)-\ln2}{x}}$ without L'Hospital's rule

Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?

Is $\frac{200!}{(10!)^{20} \cdot 19!}$ an integer or not?

Suppose $x$ and $y$ are real numbers and $x^2+9y^2-4x+6y+4=0$. Then find the maximum value of $\left(\frac{4x-9y}{2}\right)$

How to calculate this hard integral $\int_0^{\infty} \frac{\arctan(x)\sqrt{\sqrt{1+x^2}-1}}{x\sqrt{1+x^2}}\,dx$?

Solving $\int\limits_{-\infty}^\infty \frac{1}{x^8+1}dx$ through Glasser's Master Theorem

Calculating the limit $\lim\limits_{x \to 0^+} \frac{\sqrt{\sin x}-\sin\sqrt{ x}}{x\sqrt{x}}$

Find real solutions in $x$,$y$ for the system $\sqrt{x-y}+\sqrt{x+y}=a$ and $\sqrt{x^2+y^2}-\sqrt{x^2-y^2}=a^2.$

Closed form of $I(t) = \int_0^{\pi/2}\frac{\cos xdx}{\sqrt{\sin^2 x+ t\cos^2 x}}$

Integrate $\int \frac{\sin x \cos x}{\sin^4x + \cos^4x} \,dx$

Inner product on a complex field defined by norms

How to proof: $\cos(10°)\cos(30°)\cos(50°)*\cos(70°)=\frac{3}{16}$

Limit of $\lim_{n\to\infty}n\cdot \sqrt[n]{\sin\left(\frac{1}{1}\right)\cdot \sin\left(\frac{1}{2}\right)\cdots\sin\left(\frac{1}{n}\right)}$

How to compute $\lim_{x\to 0}\frac{\sin(x^2+x)-x}{x^2}$ without L'Hospital's Rule or series?

Calculate $\lim_{x \to 0} (\cot^3(x)·x·(\ln(1+3x)-3x))$

How does the first equation transform to the second one?

Area of ellipse which is not in standard form

Factorising 4th degree polynomial

Find the limit of $\lim\limits_{x\to0^+}\frac{1}{e} \frac{e- e^ \frac{\ln (1+x)}{x}}{x}$ as $x$

How to solve $\int \cot^3 x\,dx$?

What is $\int \frac{ \sqrt{(a^2 - x^2)}}{x^2}$?

Prove that: $\tan (2\tan^{-1} (x))=2\tan (\tan^{-1} (x)+\tan^{-1} (x^3))$

Singular Conics and Intersection of Line with a Conic

Evaluate $\int \frac{\cos 2x \: dx}{3 \sin x+4 \cos x}$

A tough limit problem involving $1/(\sin x - \sin a)$ and its generalization

Linear Algebra- Systems of Linear Equations