Question

integral por partes de arcsen x dx

Answer 1

            $\displaystyle \int \arcsin x\,dx=x\arcsin x-\int x\,d\arcsin x\\ \\ \int \arcsin x\,dx=x\arcsin x-\int x\cdot \dfrac{1}{\sqrt{1-x^2}}\,dx\\ \\ \int \arcsin x\,dx=x\arcsin x-\int \dfrac{x}{\sqrt{1-x^2}}\,dx\\ \\ \\ \boxed{\int \arcsin x\,dx=x\arcsin x+\sqrt{1-x^2}+C}$