Find the exact values of the integrals given below:

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Find the exact values of the integrals given below: (a) ∫5e5xe5x+4 dx\displaystyle\int \dfrac{5e^{5x}}{e^{5x}+4}\,dx (b) Using your result from part (a), determine ∫0ln⁡255e5xe5x+4 dx\displaystyle\int_{0}^{\frac{\ln 2}{5}} \dfrac{5e^{5x}}{e^{5x}+4}\,dx.

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