Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 20666 by NECx last updated on 31/Aug/17

$$\int \cot {}^{4}xdx$$

Answered by Joel577 last updated on 31/Aug/17

$${\mathrm{cosec}}^{2}x-{\cot }^{2}x=1$$$$I=\int {\cot }^{2}x({\mathrm{cosec}}^{2}x-1)dx$$$$=\int \left({\cot }^{2}x{\mathrm{cosec}}^{2}x\right)dx-\int {\cot }^{2}xdx$$$$\mathrm{Let}u=\cot x\to du=-{\mathrm{cosec}}^{2}xdx$$$$I=\int u^2.{\mathrm{cosec}}^{2}x.\frac{du}{-{\mathrm{cosec}}^{2}x}-\int ({\mathrm{cosec}}^{2}x-1)dx$$$$=-\frac{1}{3}{u}^3+\cot x+x+C$$$$=-\frac{1}{3}{\cot }^{3}x+\cot x+x+C$$

Commented by NECx last updated on 31/Aug/17

$$thankyousir.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com