If $A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$ where $a=7^x, b=7^{7^x}, c=7^{7^{7^x}}$ then $\int|A| d x$, (Where $|A|$ is the determinant of the matrix $A$ ) is equal to
- A
$\frac{7^{7^x}}{(\log 7)^3}+\mathrm{k}$, where k is constant of integration
- B
$\frac{7^{7^{7^x}}}{\log 7}+\mathrm{k}$, where k is constant of integration
- C
$\frac{7^{7^{7^x}}}{(\log 7)^3}+\mathrm{k}$, where k is constant of integration
- D
$7^{7^{7^x}}(\log 7)^3+\mathrm{k}$, where k is constant of integration
✓ Correct answer: C
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