query: Find the antiderivative for $f(x)=\frac{1}{1+\cos^2x}$
positive_passages.docid: 133337
positive_passages.text: A little integration paradox
negative_passages.docid: 125764
negative_passages.text: Under what conditions does Mathematica give a natural antiderivative when integrating?
negative_passages.docid: 74100
negative_passages.text: How do you solve $f'(x) = f(f(x))$?
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 146594
negative_passages.text: Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
negative_passages.docid: 153886
negative_passages.text: Existence of antiderivative on a part $I$ of $\mathbb{R}$
negative_passages.docid: 24358
negative_passages.text: Finding $\int \frac{dx}{a+b \cos x}$ without Weierstrass substitution.
negative_passages.docid: 116219
negative_passages.text: How can I find  $\int\frac1{\sqrt[4]{1+x^4}}\mathrm dx$?
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
negative_passages.docid: 6830
negative_passages.text: Find $\int\frac1x\sqrt\frac{1-x}{1+x}\ dx$
negative_passages.docid: 41226
negative_passages.text: Find $f:f(xf(x)+f(y))=f(x)^2+y$
negative_passages.docid: 61486
negative_passages.text: Show that $f$ is not differentiable at $(0,0)$ - $\frac{x_1^2x_2}{x_1^2+x_2^2}$
negative_passages.docid: 34790
negative_passages.text: Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
negative_passages.docid: 67907
negative_passages.text: Evaluating $\int_{-a}^a \frac{f(x)+1}{b^x+1}\,\mathrm dx$ for a $y$-axis symmetrical function $f$
negative_passages.docid: 134835
negative_passages.text: What is exactly the inverse of the function $f(x)=\frac{x}{1-x^2}$?
negative_passages.docid: 76311
negative_passages.text: $f'' + f =0$: finding $f$ using power series
negative_passages.docid: 64339
negative_passages.text: Find $f$ where $f'(x) = f(1+x)$