query: Find the indefinite integral $\int_{} \frac{t^3 dt}{\sqrt{1+t^2}}$
positive_passages.docid: 141688
positive_passages.text: Indefinite integral of $ \int \frac{x^3}{\sqrt{x^2+1}} \,\text{d}x$.
negative_passages.docid: 71611
negative_passages.text: Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$
negative_passages.docid: 83801
negative_passages.text: Finding $\int \frac {dx}{\sqrt {x^2 + 16}}$
negative_passages.docid: 137625
negative_passages.text: Need a hint to evaluate the indefinite integral $\int\frac{e^x(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$?
negative_passages.docid: 39629
negative_passages.text: Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$
negative_passages.docid: 81057
negative_passages.text: Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
negative_passages.docid: 143585
negative_passages.text: Solve the integral $\frac 1 {\sqrt {2 \pi t}}\int_{-\infty}^{\infty} x^2 e^{-\frac {x^2} {2t}}dx$
negative_passages.docid: 88815
negative_passages.text: Integral of $\int \frac{dx}{\sqrt{x^2 -9}}$
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 64743
negative_passages.text: How do I evaluate the integral $\int \frac{1}{x^3 -1}dx$
negative_passages.docid: 55738
negative_passages.text: Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
negative_passages.docid: 53519
negative_passages.text: Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
negative_passages.docid: 114505
negative_passages.text: Initial value problem $t\frac{dx}{dt}=x+\sqrt{t^2+x^2}$
negative_passages.docid: 67830
negative_passages.text: Evalute the definite integral: $\int_{0}^{3} (x^2+1) d[x]$
negative_passages.docid: 16712
negative_passages.text: Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$
negative_passages.docid: 133851
negative_passages.text: How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
negative_passages.docid: 63576
negative_passages.text: Evaluate the integral $\int \frac{\sec x}{\sqrt{3+\tan x}}dx$