query: Why is $\int \sec x\,dx$ equal to $\ln | \sec x + \tan x |$?
positive_passages.docid: 18841
positive_passages.text: Ways to evaluate $\int \sec \theta \, \mathrm d \theta$
negative_passages.docid: 23397
negative_passages.text: Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$
negative_passages.docid: 120245
negative_passages.text: Use integration by parts to express $I(2n) =$ Integral of $\tan^{2n}x\mathrm{d}x$ in terms of $I(2n − 2)$.
negative_passages.docid: 109790
negative_passages.text: Finding the value of $\int_0^{\pi/2} \frac{dt}{1+(\tan(x))^{\sqrt{2}}}$
negative_passages.docid: 126654
negative_passages.text: What is the definite integral $\int_{-1}^1 \frac{1}{x} dx$ equal to?
negative_passages.docid: 88989
negative_passages.text: Why $x<\tan{x}$ while $0<x<\frac{\pi}{2}$?
negative_passages.docid: 128607
negative_passages.text: Integral $\int\frac{(\ln x)^{10}}{x}\,dx$
negative_passages.docid: 129319
negative_passages.text: Weird "hidden answer" in $2\tan(2x)=3\text{cot}(x)$
negative_passages.docid: 47425
negative_passages.text: Finding $\int \sec^3x\,dx$
negative_passages.docid: 47206
negative_passages.text: $-1 = 0$ by integration by parts of $\tan(x)$
negative_passages.docid: 50509
negative_passages.text: Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
negative_passages.docid: 48881
negative_passages.text: Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
negative_passages.docid: 19561
negative_passages.text: Why is $\frac{1}{\frac{1}{X}}=X$?
negative_passages.docid: 123920
negative_passages.text: How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
negative_passages.docid: 10289
negative_passages.text: Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$
negative_passages.docid: 27195
negative_passages.text: Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
negative_passages.docid: 109416
negative_passages.text: How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?