Question

`int x^2 e^(x^3) dx` equals

विकल्प

• `1/3 e^(x^3) + C`

• `1/3 e^(x^4) + C`

• `1/2 e^(x^3) + C`

• `1/2 e^(x^2) + C`

Answer 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`

Answer 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`