Given, nbsp;I=∫x^2e^x dx Using Integration by parts method we have, I=∫x^2e^x dx=x^2∫e^xdx ∫dx^2dx(∫e^xdx) dx ⇒ I= x^2e^x 2∫xe^x dx ⇒ I= x^2e^x 2[x∫e^xdx ...

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Standard XII

Physics

Antiderivative

Evaluate ∫x2e...

Question

Evaluate $\int x^{2} e^{x} d x$

x^{2} e^{x} + 2 e^{x} (x + 1)

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x^{2} e^{x} - 2 e^{x}

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x^{2} e^{x} - 2 e^{x} (x - 1)

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2 e^{x} (x - 1)

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Solution

The correct option is C $x^{2} e^{x} - 2 e^{x} (x - 1)$
Given, $\int x^{2} e^{x} d x$
Using Integration by parts method we have,
$\int x^{2} e^{x} d x = x^{2} \int e^{x} d x - \int \frac{d x^{2}}{d x} (\int e^{x} d x) d x$
$\Rightarrow x^{2} e^{x} - 2 \int x e^{x} d x$
$\Rightarrow x^{2} e^{x} - 2 [x \int e^{x} d x - \int (\frac{d x}{d x} \int e^{x} d x) d x]$
$\Rightarrow x^{2} e^{x} - 2 (x e^{x} - \int e^{x} d x)$
$\Rightarrow x^{2} e^{x} - 2 e^{x} (x - 1)$

Suggest Corrections

Evaluate ∫x2ex dx

The correct option is C x2ex−2ex(x−1)Given, ∫x2ex dx Using Integration by parts method we have, ∫x2ex dx=x2∫exdx−∫dx2dx(∫exdx) dx ⇒ x2ex−2∫xex dx ⇒ x2ex−2[x∫exdx−∫(dxdx∫exdx) dx] ⇒ x2ex−2(xex−∫exdx) ⇒ x2ex−2ex(x−1)

Evaluate $\int x^{2} e^{x} d x$