The value of the definite integral - 2 2 x 3 ln ( 1 x + 3 x + 5 x + 15 x ) d x =

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Solution

Q.
The value of the definite integral $\int_{- 2}^{2} x^{3} \ln (1^{x} + 3^{x} + 5^{x} + 15^{x}) d x =$

1 $\frac{\ln 15}{4}$

2 $\frac{64}{5} \ln 15$

3 $\frac{32}{5} \ln 15$

4 $\frac{64}{5} \ln 30$

Ans.
(3)

$I = \int_{- 2}^{2} {(- x)}^{3} \ln (\frac{15^{x} + 5^{x} + 3^{x} + 1^{x}}{15^{x}}) d x$

$2 I = \int_{- 2}^{2} x^{4} \ln 15 d x$

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