query: How to solve this integral $\displaystyle \dfrac{\int_{0}^{1}{(1-x^{50})^{100}}dx}{\int_{0}^{1}{(1-x^{50})^{101}}dx} =$?
positive_passages.docid: 143368
positive_passages.text: Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$
negative_passages.docid: 42758
negative_passages.text: How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
negative_passages.docid: 107119
negative_passages.text: A logarithmic integral $\int^1_0 \frac{\log\left(\frac{1+x}{1-x}\right)}{x\sqrt{1-x^2}}\,dx$
negative_passages.docid: 133430
negative_passages.text: How to solve $x^x=100$?
negative_passages.docid: 130935
negative_passages.text: Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
negative_passages.docid: 24589
negative_passages.text: Integral of $1/(x^2-1)^2$
negative_passages.docid: 77053
negative_passages.text: Evaluating $\int_{0}^{1}\frac{\arcsin{\sqrt{x}}}{x^4-2x^3+2x^2-x+1}\operatorname d\!x$
negative_passages.docid: 95068
negative_passages.text: Integral of $\frac{1}{2x}$
negative_passages.docid: 45872
negative_passages.text: Integration: $\int\frac{1}{(x^2+x+1)^{1/2}} dx$
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 117587
negative_passages.text: $\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
negative_passages.docid: 104691
negative_passages.text: Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
negative_passages.docid: 109416
negative_passages.text: How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
negative_passages.docid: 106878
negative_passages.text: How to integrate $\int \frac{e^x dx}{1\,+\,e^{2x}}$
negative_passages.docid: 110731
negative_passages.text: How to compute $\int_{0}^{1}\int_{0}^{1} \frac{x-y}{(x+y)^3} dxdy$
negative_passages.docid: 148613
negative_passages.text: Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
negative_passages.docid: 109640
negative_passages.text: How do i find $(1+i)^{100}?$