第一题,双曲变换,令x=sinh(t),...===》
积分=(1/4)*x*(1+x^2)^(3/2)+(3/8)*sqrt(1+x^2)*x+(3/8)*arcsinh(x)
第二题:
积分= -(1/2)*sqrt(y)*(1-y)^(3/2)+(1/4)*sqrt(y)*sqrt(1-y)+(1/8)*sqrt((1-y)*y)*arcsin(-1+2*y)/(sqrt(y)*sqrt(1-y))
建议,这类积分不需要做很多,每个花费的时间太长。若能行,最好用数学软件,我所知道可视化效果最好的是Maple
![](https://iknow-pic.cdn.bcebos.com/8c1001e93901213fbd010c3c55e736d12f2e951b?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)