(10 x^9+10^x _ e ^ 10 ) d x x^ 10 +10^x = - Vidyadip

MCQ

$\int \frac{\left(10 x^9+10^x \log _{ e }^{10}\right) d x}{x^{10}+10^x}=\ldots \ldots$

A
$10^x-x^{10}+c$
B
$10^x+x^{10}+c$
C
$\left(10^x-x^{10}\right)^{-1}+c$
✓
$\log \left(10^2+x^{10}\right)+c$

✓

Answer

Correct option: D.

$\log \left(10^2+x^{10}\right)+c$

$ I =\int \frac{10 x^9+10^x \log _e{ }^{10}}{x^{10}+10^x} d x $
ધારોકે $ ₹\ x^{10}+10^x=t $
$\Rightarrow\left(10 x^9+10^x \log _{ e } 10\right) d x=d t $
$ I =\int \frac{10 x^9+10^9 \log _e{ }^{10}}{x^{10}+10^x} d x $
$=\int \frac{1}{t} d t \text { } $
$=\log |t|+ c $
$=\log \left|x^{10}+10^x\right|+c \quad\left(\because t=x^{10}+10^x\right)$
વિકલ્પ $(D)$ આવે.

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