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Question

Question: The value of l for which \(\int_{}^{}\frac{4x^{3} + \lambda 4^{x}}{4^{x} + x^{4}}\)dx = log (4<sup>x...

The value of l for which 4x3+λ4x4x+x4\int_{}^{}\frac{4x^{3} + \lambda 4^{x}}{4^{x} + x^{4}}dx = log (4x + x4) is –

A

1

B

log e 4

C

log 4 e

D

4

Answer

log e 4

Explanation

Solution

4x + x4 = t

̃ (4x3 + 4x ln e4) dx = dt

\ dtt\int \frac { \mathrm { dt } } { \mathrm { t } } = log |t| + c