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Answer to Question #5677 in Calculus for mr1pashe

Question #5677
what's integral of y=(e^x)(lnx)?
Expert's answer
Integrating by parts
<img style="width: 452px; height: 39px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmQAAAA1CAIAAABgPmCQAAAHWklEQVR4nO2d24GDIBBFU5cFUY/V0IzF7H6YREAeA4GRxHO+drNRhuHiBUT38QcAAABZHlcHAAAAMDuYJQAAQAHMEgAAoABmCQAAUACzBAAAKIBZAgA0YM3jsazb1WGAEjObpTWPHQQJVaAcGKqBbV1Q2O2Y1Sy3ddl1+P4BQALKgaEaeM8nrcEsb8WkZmkNKoQWUA4oaQCzvBlTmuW2Lo+HsVeHAV8HygE1DWCWN2NKs+TGObSBckBNA5jlzZjRLK15MD2ABlAO6GkAs7wZE5rlti5oEBpAOaCoAczyZkxolmgQ2kA5oKgB5HYz5jPL/REm1tKgFpQDmhrALG8GZgm/AsoBzBKGMZ9ZIkFoA+WApgbQ282Yziz3oSEShFpQDqho4HjXnQMLGr8PZtmdT5/z4sH6NqZRTv8H/ZCEkGk0AD+IzCzdsdTgPru//1hUiGJUsWIjXbLuGS+3quGSzpVP13sV3IPcQ3m9m3rOy3aFcmIkax0vJ/5XTwCd06UqCTSQ1UBzaLM4+Te0b3QG70eXe1Co3F9qx6DimeWHMhRTV45WVAHRLFem3hpj/7Z1eRi7rYux+wfeFy7sWa/Xa+4B+kHN0JEidNBCqtYh8T4aEUDndOlKAg10ruRkzwF/Qfue92v5nyQyWlODij5VZ5YKGWwwS/12jSS4caUs238utcv4itbEC4JdBk6ydbxYq/UYQJXRlQQa6MpkZvkF7Rvb3CwayVaFL+1UUrPUaufn1FtY14vUF/nHP60XsfxxEyzG9hkTKFCnnMJZCkmP6C7eVP3TdcViLBrow6RmOXH71j8J1Ba8rFcJzVKtmetGdamJpb/wHr9b8Pz0/WF+UOqsn5u1drktcnN1W1f7Z83D2OdiyLaaxD2wsWl//49cvyBr3is0XsVcLbr3PY4qHl92c2bd34fUqEo5lbUODnksS9gdEgIYkK4BkkADQg00kJSNYma+t32zrRDbPHLuHZkInW+JepXQLNWWO+vlHlv5MvZVffuas/vftcb5zi6YTO283Tex+/6ZsYR7rPM1J5zcRoKxgxRPikegzvj8pMdg4Bb0jXi/Oz4YcB8oKEqQq9Zae+oJikq104B0dZYEGhDWujmctGw0MvPd7RvJoHfusDPEfUoSocQtK3bD5k/ljqDiiGRXswUtH1Vwpngy9uxnrTIUR6zU5FgiKLV+VpA94sOcB1GLrsLhKkf5HMc3tnUZOEuWKqeh1qfmPR2UEsCIdKUl0aAHNPA3bEhalo0sM5908y9vX3dN7sl5Se8oMF29YoSSzIjMUnGtvcYss9PdIObEUrYzwEpwqnvsTIJFuMbNBwOn9N58WVpWrCPll0Gczp48d4+RllA5DbU+HfKZWX6arp6SQAPHB5KU5gMslBK/jpYz8wGztG9r45ZmlkEsudpJulUPs1RbhK1ylGqvjKWilCKRV2Zn/wctGRx40zIu4EJhLR1JZ7QlVE5DrZXNUrJk0iuXaEBc67ZgymY5NDPf3r7FO8dysxStROalIzFLkVf2WYYtz/T8r4ZaTK26Ji4w5eLCuscTHv+0wxhDstLcmvOm8Fo60rYuy7oOHnBJldNQa8FVT3jPske6SvfHq/SABsYhNMtyZj7o5t/evh3NshRhn5ml4iJsjVmeKufetw2ylpz5GZtYn40fmQwvWkAkwtiO1xwDJ5ZlISYPqupI1jy/f7549ESqnIZanw85V0W0EN8lXV0lgQbGIZHN6Mx8e/vG4vf251Tcs8xH2OeepXiHWQ/khYVXJ+/32CapZd2cnB0/vg90/hYE9DyTNfvQJDyTV0IYoz/XNbYqjSO98u+8anW+JRA/JFBnePM/ecaKNfZqKpXzSa2fI/3zHodz6f3T1VsSaOAcYy9KstHIzHe3b8QsvQ4Qi+VcuCRCSb8qmKV7203jpqVQ7omFidQi7HGAsX+nDL/qmJ6+uwnwzhR+LdpMYXByBnvlqwhxCztqeA0YvMo5JzM2TFzw195Ujemqau2c/nXA+7dwgd4714h0jZAEGhh2bUvLRjEz39q+ka2wXiin2P4S642pCIMcFYUz2X8d2auiNI3tTGFBtxoFq/whJlBObwGcQRJZJtAAXExbJ5R1rCnNUmMOO4R+Owe4LFYyh3JGbh1BEiXm0ABcS71dSnsWZtmbj/dDjZ+g/CLzKGfAhjgkIWIeDcCl1IxZK8agc5ml6mYi+CFQDqABOBCMWWvHoDOaJUNDqAXlgIIGnD0nzl5BLPoeYJbwC6AcuOTxSe+pP/hp5jLLsc8sw++CckBNA8ctsW3oe+FhLiY0S8ZpUA3KAUUNvJ/WQ3I3Yiqz1HyxHvwSKAd0NYDi7sdUZsmTZNAGygFNDai8Fx4mYyaz5GkyaAPlgKIGlN4LD5Mxk1mOeZsx/D4oB7Q0oPdeeJiMiczSGgZp0ALKARUN6L4XHibjcrN8iZznlaAOlANoAPSYwSwZmkEDKAfQAOhxuVkCAADMDmYJAABQALMEAAAogFkCAAAUwCwBAAAK/AMO6weQve2BwAAAAABJRU5ErkJggg==" alt="">
where Ei(x) - the exponential integral
<img style="width: 110px; height: 67px;" src="data:image/png;base64,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" alt="">

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