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Question
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Options
`(3)^("x"^3) + "c"`
`(3)^("x"^3)/(3 * log 3) + "c"`
`log 3 (3)^("x"^3)` + c
`"x"^2 (3)^("x"^3) + "c"`
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Solution
`(3)^("x"^3)/(3 * log 3) + "c"`
Explanation:
Let I = `int "x"^2 * (3)^("x"^3) "dx"`
Put x3 = t
∴ `3"x"^2 "dx" = "dt"`
∴ `"x"^2 "dx" = 1/3 "dt"`
∴ I = `1/3 int 3^"t" * "dt"`
`= 1/3 * 3^"t"/log 3` + c
`= (3)^("x"^3)/(3 log 3)` + c
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