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Question Number 131176 by Raxreedoroid last updated on 02/Feb/21

$$\int \frac{cos\left(ln\left(a^x\right)\right)}{\sqrt{k}}dx=??$$

Answered by Ar Brandon last updated on 02/Feb/21

$$\mathrm{I}=\int \frac{\cos \left({\mathrm{lna}}^{\mathrm{x}}\right)}{\sqrt{\mathrm{k}}}\mathrm{dx},\mathrm{t}={\mathrm{lna}}^{\mathrm{x}}\Rightarrow \mathrm{dt}=\mathrm{lnadx}$$$$=\int \frac{\cos \left(\mathrm{t}\right)}{\sqrt{\mathrm{k}}\mathrm{lna}}\mathrm{dt}=\frac{\sin \left({\mathrm{lna}}^{\mathrm{x}}\right)}{\left(\mathrm{lna}\right)\sqrt{\mathrm{k}}}+\mathrm{C}$$

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