mhd.math

### Questions (76)

 44 Is there a function with the property$f(n)=f^{(n)}(a)$ 29 Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$ 19 Finding the fraction $\frac{a^5+b^5+c^5+d^5}{a^6+b^6+c^6+d^6}$ when knowing the sums $a+b+c+d$ to $a^4+b^4+c^4+d^4$ 15 integral of $\int \limits_{0}^{\infty}\frac {\sin (x^n)} {x^n}dx$ 13 closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$

### Reputation (3,460)

 +20 Why does the series $\sum_{n=1}^\infty\frac1n$ not converge? +5 show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$ -2 Why does Wolfram Alpha say that $\sqrt{1}=-1$? +5 integral of $\int \limits_{0}^{\infty}\frac {\sin (x^n)} {x^n}dx$

### Answers (54)

 12 How to evaluate the integral $\int e^{x^3}dx$ 11 Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ 10 Why does the series $\sum_{n=1}^\infty\frac1n$ not converge? 8 Evaluating $\displaystyle\int_0^1\frac{\sqrt{1-y^2}}{1+y^2}dy$ without trig substitution 8 How to evaluate the integral $\int e^{x^3}dx$

### Tags (66)

 74 calculus × 44 11 problem-solving 49 integration × 40 11 recreational-mathematics 23 sequences-and-series × 11 10 trigonometry × 7 14 limits × 14 10 harmonic-numbers 11 infinite-product × 3 8 real-analysis × 5

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