(\integral\_{}^{}7^{7^{7^{x}}}). (7^{7^{x}}) . 7x dx is equa... | MATH - FUNDAMENTAL INTEGRATION | SolveeIt

$\int_{}^{}7^{7^{7^{x}}}$ . $7^{7^{x}}$ . 7^x dx is equal to –

$\frac{7^{7^{7^{x}}}}{(\log_{e}7)^{3}}$ + c

$\frac{7^{7^{7^{x}}}}{(\log_{e}7)^{3}} + 7$ + c

$7^{7^{7^{x}}}$ . (log_e 7)³ + c

None of these

Answer

$\frac{7^{7^{7^{x}}}}{(\log_{e}7)^{3}}$ + c

Explanation

We have, $\int_{}^{}7^{7^{7^{x}}}$ . $7^{7^{x}}$ . 7^x dx

= $\frac { 1 } { \left( \log _ { e } 7 \right) ^ { 3 } }$ $\int_{}^{}\left( 7^{7^{7^{x}}}\log_{e}7 \right)$ . $\left( 7^{7^{x}}\log_{e}7 \right)$

$\left( 7 ^ { x } \log _ { e } 7 \right)$ dx

= $\frac { 1 } { \left( \log _ { e } 7 \right) ^ { 3 } }$ $\int_{}^{}1$ . d( $7^{7^{x}}$ ) = $\frac{7^{7^{7^{x}}}}{(\log_{e}7)^{3}}$ + c.

Hence (1) is the correct answer.

Question: \(\int_{}^{}7^{7^{7^{x}}}\). \(7^{7^{x}}\) . 7<sup>x</sup> dx is equal to –...