Question

∫(x²e^x)/(x+2)²dx

Answer 1

∫(x²e^x)/(x+2)²dx
=∫(x²+4x+4-4x-8+4)e^x/(x+2)²dx
=∫((x+2)²-4x-8+4)e^x/(x+2)²dx
=∫(x+2)²e^x/(x+2)²dx
-
4∫(x+2)e^x/(x+2)²dx
+
4∫e^x/(x+2)²dx
=∫e^xdx
-
4∫e^x/(x+2)dx
+
4∫e^x/(x+2)²dx
=e^x
-
4∫1/(x+2)d(e^x)
+
4∫e^x/(x+2)²dx
=e^x
-
4e^x/(x+2)
-
4∫(e^x)/(x+2)²
+
4∫e^x/(x+2)²dx
=e^x
-
4e^x/(x+2)
+
C
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