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Question
`int x^2 e^(x^3) dx` equals
Options
`1/3 e^(x^3) + C`
`1/3 e^(x^4) + C`
`1/2 e^(x^3) + C`
`1/2 e^(x^2) + C`
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Solution 1
`bb(1/3 e^(x^3) + C)`
Explanation:
`int x^2 e^(x^3) dx` put x3 = t
∴ 3x2 dx = dt
= `1/3 int (3x^2) e^(x^3) dx`
= `1/3 int e^t dt`
= `1/3 e^t + C`
= `1/3 e^(x^3) + C`
Solution 2
`bb(1/3 e^(x^3) + C)`
Explanation:
Given `int x^2 e^(x^3) dx`
Put x3 = y
⇒ 3x2dx = dy
Then `int x^2 e^(x^3) dx = 1/3 int e^y dy`
= `1/3 e^y + C`
= `1/3 e^(x^3) + C`
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