query: Applying substitution to $\int \sqrt{1+\sin(x)}$
positive_passages.docid: 24808
positive_passages.text: How to evaluate the integral $\int \sqrt{1+\sin(x)} dx$
negative_passages.docid: 67629
negative_passages.text: How to evaluate these indefinite integrals with $\sqrt{1+x^4}$?
negative_passages.docid: 65975
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$
negative_passages.docid: 71611
negative_passages.text: Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$
negative_passages.docid: 23685
negative_passages.text: Integrating $\int \sin^n{x} \ dx$
negative_passages.docid: 99584
negative_passages.text: Evaluation of $\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$
negative_passages.docid: 118586
negative_passages.text: Confused About Trigonometric Substitution
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 124677
negative_passages.text: Substitution needed for calculating an integral
negative_passages.docid: 140860
negative_passages.text: Variable substitution when integrating with Mathematica
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
negative_passages.docid: 26444
negative_passages.text: How can I integrate $\ln \left( x+\sqrt{1+x^2} \right) $?
negative_passages.docid: 104583
negative_passages.text: Simplify $\int \frac{1}{\sqrt{2-x^2}}\, dx$
negative_passages.docid: 143734
negative_passages.text: Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
negative_passages.docid: 138230
negative_passages.text: Evaluate $ \int^{\frac{\pi}{2}}_0 \frac{\sin x}{\sin x+\cos x}\,dx $ using substitution $t=\frac{\pi}{2}-x$
negative_passages.docid: 4693
negative_passages.text: what is the$ \int \sin (x^2) \, dx$?
negative_passages.docid: 16800
negative_passages.text: Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$