User A is for Ambition - Mathematics Stack Exchange

64 votes

7 answers

72k views

Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $ [closed]

asked Jun 10, 2014 at 1:30

20 votes

10 answers

2k views

What is the most efficient method to evaluate this indefinite integral?

asked Jun 12, 2014 at 23:22

10 votes

1 answer

2k views

Fundamental Theorem of Calculus: Why Doesn't the Integral Depend on Lower Bound?

asked Jan 1, 2015 at 6:01

9 votes

1 answer

243 views

For which integers $1\leq{m}\leq{10}$ is it true that $\int_0^\pi{(\cos{x})(\cos{2x})\cdots(\cos{mx})}\,dx = 0$?

asked Jan 18, 2015 at 3:23

9 votes

2 answers

763 views

How to Solve Trigonometric Equations?

asked Jan 23, 2015 at 8:22

8 votes

2 answers

870 views

Solve $(\alpha,\beta)$ for $\lim_{n\to\infty} \frac{\sqrt[n^2]{1!2!\cdots n!}}{n^\alpha} = \beta$

asked Jan 29, 2015 at 5:36

7 votes

5 answers

227 views

Solve $\int_0^\infty \frac{\ln x}{x^2+4} \,\mathrm{d}x$

asked Jan 28, 2015 at 12:47

6 votes

4 answers

2k views

Find All Dimensions such that Volume of Box = Surface Area

asked Mar 20, 2015 at 18:42

5 votes

2 answers

423 views

Evaluate $\lim_{n \to \infty}\Bigl[\bigl(\prod_{k=1}^{n}{\frac{2k}{2k-1}}\bigr)\bigl(\int_{-1}^{\infty}\frac{(\cos{x})^{2n}}{2^x}\,dx\bigr)\Bigr]$

asked Jan 2, 2015 at 5:26

4 votes

1 answer

674 views

Find the largest value of x given the equation...

asked Oct 11, 2014 at 2:49

4 votes

1 answer

8k views

Difficult Polynomial Question

asked Oct 11, 2014 at 7:40

4 votes

2 answers

534 views

Rearranging a Staircase Grid into a Square

asked Mar 23, 2015 at 21:21

4 votes

6 answers

15k views

How to Find the Function of a Given Power Series?

asked Apr 23, 2015 at 22:32

4 votes

1 answer

178 views

Lebesgue measurable function in $\mathbb{R}^d$ is almost everywhere pointwise limit of step functions (Stein & Shakarchi, Real Analysis)

asked Mar 14, 2023 at 23:20

3 votes

3 answers

2k views

Finding the Limit of the Ratio of a Recursive Sequence's Terms

asked Apr 23, 2015 at 4:33

3 votes

3 answers

316 views

Split 16 Consecutive Integers into Two Subsets of 8 Integers

asked May 2, 2015 at 11:16

3 votes

1 answer

198 views

Sums of Pairs of Integers

asked Apr 2, 2015 at 3:39

3 votes

2 answers

242 views

Find $\int_0^a{f(x)}\, dx$

asked Jan 24, 2015 at 13:13

3 votes

3 answers

8k views

Recommended Books for AIME/USAMO Preparation?

asked Dec 28, 2014 at 2:13

3 votes

2 answers

213 views

Need Help Solving this Indefinite Integral

asked Jun 7, 2014 at 17:11

3 votes

2 answers

5k views

Difficult Indefinite Integral

asked Jun 8, 2014 at 0:20

3 votes

1 answer

207 views

Evaluate Indefinite Integral

asked Jun 9, 2014 at 19:45

2 votes

3 answers

328 views

Stuck on Indefinite Integral

asked Jun 15, 2014 at 11:24

2 votes

2 answers

2k views

Stars & Bars Question: Identical Balls in Distinct Boxes

asked Dec 28, 2014 at 1:24

2 votes

4 answers

94 views

Simplify $f(x) = \sum_{n=0}^{\infty}{\frac{\sin{(nx)}}{n!}}$

asked Jan 16, 2015 at 9:04

2 votes

1 answer

668 views

Most Common Difference Between Two Consecutive Primes?

asked Apr 24, 2015 at 2:29

2 votes

1 answer

242 views

What are the odds that two people are friends in a network of 20 people?

asked Apr 25, 2015 at 2:38

2 votes

4 answers

222 views

Given $\int_0^x (x-t+1)g(t)\,\mathrm{d}t = x^4 + x^2,$ Find $g(x)$

asked Jan 28, 2015 at 22:23

2 votes

1 answer

149 views

Splitting a Set of Consecutive Cubes into Equal Subsets

asked Apr 1, 2015 at 0:59

2 votes

1 answer

632 views

Trouble Understanding Counting Problem

asked Apr 1, 2015 at 5:04

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41 Questions

Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $ [closed]

What is the most efficient method to evaluate this indefinite integral?

Fundamental Theorem of Calculus: Why Doesn't the Integral Depend on Lower Bound?

For which integers $1\leq{m}\leq{10}$ is it true that $\int_0^\pi{(\cos{x})(\cos{2x})\cdots(\cos{mx})}\,dx = 0$?

How to Solve Trigonometric Equations?

Solve $(\alpha,\beta)$ for $\lim_{n\to\infty} \frac{\sqrt[n^2]{1!2!\cdots n!}}{n^\alpha} = \beta$

Solve $\int_0^\infty \frac{\ln x}{x^2+4} \,\mathrm{d}x$

Find All Dimensions such that Volume of Box = Surface Area

Evaluate $\lim_{n \to \infty}\Bigl[\bigl(\prod_{k=1}^{n}{\frac{2k}{2k-1}}\bigr)\bigl(\int_{-1}^{\infty}\frac{(\cos{x})^{2n}}{2^x}\,dx\bigr)\Bigr]$

Find the largest value of x given the equation...

Difficult Polynomial Question

Rearranging a Staircase Grid into a Square

How to Find the Function of a Given Power Series?

Lebesgue measurable function in $\mathbb{R}^d$ is almost everywhere pointwise limit of step functions (Stein & Shakarchi, Real Analysis)

Finding the Limit of the Ratio of a Recursive Sequence's Terms

Split 16 Consecutive Integers into Two Subsets of 8 Integers

Sums of Pairs of Integers

Find $\int_0^a{f(x)}\, dx$

Recommended Books for AIME/USAMO Preparation?

Need Help Solving this Indefinite Integral

Difficult Indefinite Integral

Evaluate Indefinite Integral

Stuck on Indefinite Integral

Stars & Bars Question: Identical Balls in Distinct Boxes

Simplify $f(x) = \sum_{n=0}^{\infty}{\frac{\sin{(nx)}}{n!}}$

Most Common Difference Between Two Consecutive Primes?

What are the odds that two people are friends in a network of 20 people?

Given $\int_0^x (x-t+1)g(t)\,\mathrm{d}t = x^4 + x^2,$ Find $g(x)$

Splitting a Set of Consecutive Cubes into Equal Subsets

Trouble Understanding Counting Problem