计算题
11.求下列不定积分
(1)∫aretanxdx (2)∫(x2+1)sinxdx (3)
(1)∫aretanxdx (2)∫(x2+1)sinxdx (3)
【正确答案】
(2)∫(x2+1)sinxdx=一∫(x2+1)dcosx
=一(x2+1)cosx+∫2xcosxdx=一(1+x2)cosx+∫2xdsinx
一(1+x2)cosx+2xsinx一∫sinxd2x=一(1+x2)cosx+2xsinx一2∫sinxdx
=一(1+x2)cosx+2xsinπ+2cosx
(2)∫(x2+1)sinxdx=一∫(x2+1)dcosx
=一(x2+1)cosx+∫2xcosxdx=一(1+x2)cosx+∫2xdsinx
一(1+x2)cosx+2xsinx一∫sinxd2x=一(1+x2)cosx+2xsinx一2∫sinxdx
=一(1+x2)cosx+2xsinπ+2cosx
【答案解析】