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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \large\frac{ax^{a-1}+a^x \log a}{x^a+a^x}$$dx$

$(a)\;x^2 +2x+c \qquad(b)\;x^a+a^x+x \qquad(c)\;\log_e[x^a+a^x]+c \qquad (d)\;\log x +c $

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A)
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$x^a+a^x=t$
differentiate both side with respect to x
$(ax^{a-1}+a^x \log _e a )dx=dt$
=> $\int \large\frac{dt}{t}$
=> $\log _e^t +c$
=> $\log _e[x^a +a^x]+c$
Hence c is the correct answer.
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