\\int3^{3^{3^{ x}}} 3^{3^{x}} 3^{x} d x

Correct Answer is : 333x(log3)3+C

{3^{3^{x}} 3^{x}}/{(\log 3)^{3}}+C

{3^{3^{3^{x}}}}/{(\log 3)^{3}}+C

NIMCET 2021 Question Paper with solutions

Question : 47 of 120

Marks: +1, -0

\∫3^{3^{3^{ x}}} 3^{3^{x}} 3^{x} d x

Solution:

\∫3^{3^{3^{ x}}} 3^{3^{x}} 3^{x} d x

=3^{3^{x}}=t

3^{3^{x}}(\log 3) \.3^{x}(\log 3)={d t}/{d x}

3^{3^{x}} 3^{x}(\log 3)^{2} \.\λx=d t

3^{3^{3}} 3^{x} \.d x={d t}/{(\log 3)^{2}}

=\∫{3^{t} \.d t}/{(\log 3)^{2}}

={3^{t}}/{\log 3} \.{1}/{(\log 3)^{2}}+c

={3^{t}}/{(\log 3)^{3}}-c

={3^{3^{x^{x}}}}/{(\log 3)^{3}}+c

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