{(10x^9+10^x_{e}10)}{x¹0}+10^x}\,dx equals

NCERT Class XII Mathematics Chapter - - Solutions

Choose the correct answer in Exercises 60 and 61.

Question : 60 of 271

Marks: +1, -0

\int \frac{(10x^9+10^x\log_{e}10)}{x^{10}+10^x}\,dx

equals

Solution:

Let

I = \int \frac{(10x^9+10^x\log_{e}10)}{x^{10}+10^x}\,dx

Put

x^{10}+10^x = t

\Rightarrow (10x^9+\log_{e}10 \cdot 10^x)\,dx = dt

\Rightarrow I = \int \frac{dt}{t} = \log|t|+C

= \log(10^x+x^{10})+C

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