MCQ
The value of $\lambda$ for which $\int {\frac{{4{x^3} + \lambda {4^x}}}{{{4^x} + {x^4}}}} \,\,dx = \log ({4^x} + {x^4}) + c$ is
- A$1$
- ✓$log_e4$
- C$log_4e$
- D$4$
$\left(4^{x} \ln 4+4 x^{3}\right) d x=d t$
$\int {\frac{{{\rm{dt}}}}{{\rm{t}}}} = \ln {\rm{t}} + {\rm{c}}$
$ = \ln \left| {{4^x} + {{\rm{x}}^4}} \right| + {\rm{c}}$
$\therefore \lambda=\ln 4$
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