query: Indefinite Integral Constant Multiple Rule
positive_passages.docid: 154580
positive_passages.text: Is indefinite integration non-linear?
negative_passages.docid: 85814
negative_passages.text: Quotient of two integrals $\frac{\int_0^\pi x^3\ln(\sin x)\,dx}{\int_0^\pi x^2\ln(\sqrt{2}(\sin x))\,dx}$
negative_passages.docid: 83531
negative_passages.text: Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
negative_passages.docid: 1366
negative_passages.text: Complex Analysis: Complex Integral
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
negative_passages.docid: 141024
negative_passages.text: Generalising integration by parts for the product of more than two functions
negative_passages.docid: 16800
negative_passages.text: Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$
negative_passages.docid: 158407
negative_passages.text: derivative bounded by a constant multiple of the function
negative_passages.docid: 15947
negative_passages.text: Validity of Substitutions in Integrals
negative_passages.docid: 19845
negative_passages.text: Mean Value Theorem for Integrals
negative_passages.docid: 67629
negative_passages.text: How to evaluate these indefinite integrals with $\sqrt{1+x^4}$?
negative_passages.docid: 146870
negative_passages.text: Integrals depending on a parameter: $\int_{0}^{\pi/2} \ln(a^2\sin^2{x} + \cos^2{x})dx $
negative_passages.docid: 24235
negative_passages.text: Is there a rule of integration that corresponds to the quotient rule?
negative_passages.docid: 37584
negative_passages.text: How many "constants of integration" will a PDE have?
negative_passages.docid: 89537
negative_passages.text: $ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
negative_passages.docid: 52744
negative_passages.text: The value of a, b and c for this integral
negative_passages.docid: 101287
negative_passages.text: Definite integral containing 2 trig functions and a square root function