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Question Number 163720 by alcohol last updated on 09/Jan/22

$${\int }_2^4\frac{\sqrt{ln(9-x)}}{\sqrt{ln(9-x)}+\sqrt{ln(3+x)}}dx$$$$$$

Answered by Mathspace last updated on 09/Jan/22

$$x=6-t\Rightarrow t=6-x\Rightarrow$$$$I={\int }_4^2\frac{\sqrt{ln(3+t)}}{\sqrt{ln(3+t)+\sqrt{ln(9-t)}}}(-dt)$$$$={\int }_2^4\frac{\sqrt{ln(3+x)}}{\sqrt{ln(3+x)}+\sqrt{ln(9-x)}}dx\Rightarrow$$$$2I={\int }_2^{4}dx=2\Rightarrow I=1$$

Commented by peter frank last updated on 11/Jan/22

$$\mathrm{great}$$

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