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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int 2^{2^{2^x}} 2^{2^x} 2^x d x$
  • ✓
    $\frac{1}{(\log 2)^3} 2^{2^{2^x}}+C$
  • B
    $\frac{1}{(\log 2)^3} 2^{2^x}+C$
  • C
    $\frac{1}{(\log 2)^2} 2^{2^x}+C$
  • D
    $\frac{1}{(\log 2)^4} 2^{2^{2^x}}+C$
✓

Answer

Correct option: A.
$\frac{1}{(\log 2)^3} 2^{2^{2^x}}+C$
(a) : Let $I=\int 2^{2^{2^x}} 2^{2^x} 2^x d x$
Let $2^{2^{2^x}}=t \Rightarrow 2^{2^{2^x}} 2^{2^x} 2^x(\log 2)^3 d x=d t$
$
\Rightarrow I=\int \frac{1}{(\log 2)^3} d t=\frac{1}{(\log 2)^3} t+C=\frac{1}{(\log 2)^3} 2^{2^{2^x}}+C
$

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