query: Why is reduction formula of $\int \cos^n (x) dx$ restricted to n>1?
positive_passages.docid: 12653
positive_passages.text: Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$
negative_passages.docid: 60761
negative_passages.text: Proof: $\cos^p (\theta) \le \cos(p\theta)$
negative_passages.docid: 37158
negative_passages.text: upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$
negative_passages.docid: 114418
negative_passages.text: A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
negative_passages.docid: 115375
negative_passages.text: Indefinite integral of $e^{x^n}$
negative_passages.docid: 96095
negative_passages.text: If $\{a_1,\dots,a_{\phi(n)}\}$ is a reduced residue system, what is $a_1\cdots a_{\phi(n)}$ congruent to?
negative_passages.docid: 39504
negative_passages.text: Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?
negative_passages.docid: 36063
negative_passages.text: Finding the limit of $(1-\cos x)/x^2$
negative_passages.docid: 144439
negative_passages.text: For a $C^1$ function, the difference $|{g'(c)} - {{g(d)-g(c)} \over {d-c}} |$ is small when $|d-c|$ is small
negative_passages.docid: 154133
negative_passages.text: Flawed proof by induction that $a^{n-1}=1$
negative_passages.docid: 11489
negative_passages.text: Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
negative_passages.docid: 83790
negative_passages.text: Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
negative_passages.docid: 46359
negative_passages.text: Finding the general integrals of functions like $\frac1{x^n+1}$, $\cos^nx$.
negative_passages.docid: 132448
negative_passages.text: Prove that: $\int_0^{n\pi}f(\cos^2(x))\,dx=n\int_0^{\pi}f(\cos^2(x))\,dx?$
negative_passages.docid: 92176
negative_passages.text: Solving $\lim_{n\to\infty}(n\int_0^{\pi/4}(\tan x)^ndx)$?
negative_passages.docid: 17188
negative_passages.text: Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer
negative_passages.docid: 133160
negative_passages.text: Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$