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 165787 by daus last updated on 08/Feb/22

$$find\int {cos}^{3}xdx?$$

Answered by aleks041103 last updated on 08/Feb/22

$${cos}^{3}x=cosx(1-{sin}^{2}x)=$$$$=cosx-{cosxsin}^{2}x$$$$\Rightarrow \int {cos}^{3}xdx=\int cosxdx-\int cosx{sin}^{2}xdx=$$$$=sinx-\int {\left(sinx\right)}^{2}d\left(sinx\right)=$$$$=sinx-\frac{1}{3}{sin}^{3}x+C$$

Answered by nurtani last updated on 08/Feb/22

$$\int {cos}^{3}xdx=\int {cos}^{2}x\cdot cosxdx$$$$=\int (1-{sin}^2)\cdot cosxdx$$$$let:u=sinx\Rightarrow \frac{du}{dx}=cosx\Rightarrow dx=\frac{du}{cosx}$$$$\int {cos}^{3}xdx=\int (1-{sin}^{2}x)\cdot cosxdx$$$$=\int (1-u^2).\cancel{cosx}\cdot \frac{du}{\cancel{cosx}}$$$$=\int (1-u^2)du$$$$=u-\frac{1}{3}{u}^3+C$$$$=sinx-\frac{1}{3}{sin}^{3}x+C$$$$\therefore \int {cos}^{3}xdx=sinx-\frac{1}{3}{sin}^{3}x+C$$

Commented by daus last updated on 08/Feb/22

$$thanks$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com