Cambridge Maths Academy

수학 모음 (Maths collection) 전체보기 Question. Evaluate the following integrals: $$ \begin{align} {\rm (a)}&& &\int\frac{1}{\sqrt{1-3x^2}}\,\textrm{d}x \\ {\rm (b)}&& &\int\frac{x}{4x^2+8x+13}\,\textrm{d}x \\ {\rm (c)}&& &\int_0^1\arcsin x\,\textrm{d}x \end{align} $$ Solution. (a) By substitution, $$ \begin{align} x&=\frac1{\sqrt{3}}\sin u \\ \Rightarrow\quad \textrm{d}x&=\frac1{\sqrt{3}}\cos u\,\textr..