- x ex2log 2 ex2 d x-A- 2 ex2-log 2 eB- 2x2 ex2-1-log 0 x2-x2C- 2x2 ex-21-log 2D- 2x2log 2 ex2-log 2

The correct option is C 2^x^2e^x^22(1+log 2)I=∫ xe^x^2log2e^x^2 dx=∫ x·2^x^2· e^x^2 dx Let x^2=t⇒ 2x dx=dt I=12∫ 2^t· e^t dt=12 (2e)^tln(2e)+c ⇒ I=2^x^2e^x^22 ...

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Byju's Answer

Standard XII

Mathematics

Theorems on Integration

∫ x ex2log 2 ...

Question

$\int x e^{x^{2} log 2} e^{x^{2}} d x =$ ____ $+ c$

\frac{(2 e)^{x^{2}}}{log (2 e)}

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\frac{2^{x^{2}} e^{x^{2}}}{1 + log 2}

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\frac{2^{x^{2}} e^{x^{2}}}{2 (1 + log 2)}

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\frac{2^{x^{2} log 2} e^{x^{2}}}{log 2}

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Solution

The correct option is C $\frac{2^{x^{2}} e^{x^{2}}}{2 (1 + log 2)}$
$I = \int x e^{x^{2} log 2} e^{x^{2}} d x = \int x \cdot 2^{x^{2}} \cdot e^{x^{2}} d x$

Let $x^{2} = t \Rightarrow 2 x d x = d t$
$I = \frac{1}{2} \int 2^{t} \cdot e^{t} d t = \frac{1}{2} \frac{(2 e)^{t}}{ln (2 e)} + c$
$\Rightarrow I = \frac{2^{x^{2}} e^{x^{2}}}{2 (1 + log 2)} + c$

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Similar questions

$\int x^{2} e^{x^{3}} d x =$

Q. If

y = \sin^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}), then \frac{d y}{d x} =

(a)

- \frac{2}{1 + x^{2}}

(b)

\frac{2}{1 + x^{2}}

(c)

\frac{1}{2 - x^{2}}

(d)

\frac{2}{2 - x^{2}}

Integrate:

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

\int_{- 1}^{1 / 2} \frac{e^{x} (2 - x^{2}) d x}{(1 - x) \sqrt{1 - x^{2}}}

is equal to

\frac{1}{2} \int - 1 \frac{e^{x} (2 - x^{2})}{(1 - x) \sqrt{1 - x^{2}}} d x

is equal to

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∫xex2log2ex2 dx= ____ +c

The correct option is C 2x2ex22(1+log2)I=∫xex2log2ex2 dx=∫x⋅2x2⋅ex2 dx Let x2=t⇒2x dx=dt I=12∫2t⋅et dt=12(2e)tln(2e)+c ⇒I=2x2ex22(1+log2)+c

$\int x e^{x^{2} log 2} e^{x^{2}} d x =$ ____ $+ c$