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 88071 by ar247 last updated on 08/Apr/20

Commented by ar247 last updated on 08/Apr/20

$$helpplease$$

Commented by jagoll last updated on 08/Apr/20

$$\mathrm{b})\mathrm{what}\mathrm{the}\mathrm{meaning}\int \frac{\mathrm{dx}}{1+\sin \mathrm{x}}\mathrm{d}?$$

Commented by ar247 last updated on 08/Apr/20

$$b)\int \frac{dx}{1+sinx}typo$$

Commented by john santu last updated on 08/Apr/20

$$iguessyourquestion$$$$b)\int \frac{dx}{1+\sin x}=\int \frac{1-\sin x}{1-\sin {}^{2}x}dx$$$$=\int \frac{1-\sin x}{\cos {}^{2}x}dx=\int \sec {}^{2}x-\sec x\tan xdx$$$$=\tan x-\sec x+c$$

Commented by ar247 last updated on 08/Apr/20

$$helpplease$$

Commented by mathmax by abdo last updated on 08/Apr/20

$$a)\int \frac{e^t}{e^{2t}-9}dt{=}_{e^t=x}\int \frac{x}{x^2-9}\frac{dx}{x}=\int \frac{dx}{x^2-9}=\frac{1}{6}\int (\frac{1}{x-3}-\frac{1}{x+3})dx$$$$=\frac{1}{6}ln\mid \frac{x-3}{x+3}\mid +C=\frac{1}{6}ln\mid \frac{e^x-3}{e^x+3}\mid +C$$

Commented by mathmax by abdo last updated on 08/Apr/20

$$b)\int \frac{dx}{1+sinx}{=}_{tan\left(\frac{x}{2}\right)=t}\int \frac{2dt}{(1+t^2)(1+\frac{2t}{1+t^2})}$$$$=\int \frac{2dt}{1+t^2+2t}=2\int \frac{dt}{{(t+1)}^2}=-\frac{2}{t+1}+C=-\frac{2}{1+tan\left(\frac{x}{2}\right)}+C$$

Answered by john santu last updated on 08/Apr/20

$$a)\int \left(\frac{e^t}{e^2-9}\right)dx?$$$$=\frac{e^{t}x}{e^2-9}+c$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com