First slide

Methods of integration

Question

$\int 5^{5^{5^{x}}} {.5}^{5^{x}} {.5}^{x} d x =$

Easy

A

$\frac{5^{5^{x}}}{{(\log 5)}^{3}} + c$
B

$5^{5^{x}} {(\log 5)}^{3} + c$
C

$5^{x} {(\log 5)}^{3} + c$
D

$\frac{5^{5^{5^{x}}}}{{(\log 5)}^{3}} + c$

Solution

                                   $5^{5^{5^{x}}} = t$
$5^{5^{5^{x}}} \log {5.5}^{5^{x}} \log {5.5}^{x} . \log 5 d x = d t$
       $\int 5^{5^{5^{x}}} {.5}^{5^{x}} {.5}^{x} d x =$    $\int \frac{1}{{(\log 5)}^{3}} d t = \frac{1}{{(\log 5)}^{3}} t + C$
                                         $= \frac{5^{5^{5^{x}}}}{{(\log 5)}^{3}} + C$

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