Category: Integration

Question Number 98831 by bramlex last updated on 16/Jun/20 Commented by john santu last updated on 16/Jun/20 $$\int \frac{2\mathrm{dx}}{{\mathrm{x}}^8(1-\frac{1}{{\mathrm{x}}^7})}=\int \frac{2\mathrm{d}(1-\frac{1}{{\mathrm{x}}^7})}{7(1-\frac{1}{{\mathrm{x}}^7})}$$$$=\:\frac{\mathrm{2}}{\mathrm{7}}\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{7}} −\mathrm{1}}{\mathrm{x}^{\mathrm{7}}…

Question Number 98821 by bramlex last updated on 16/Jun/20 $$\int {\stackrel{\mathrm{\infty }}{}}_0\frac{dx}{a^2+x^2}=?$$ Answered by Ar Brandon last updated on 16/Jun/20 $$\left.\mathcal{I}=\frac{\mathrm{1}}{\mathrm{a}}\left[\mathrm{arctan}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\right]_{\mathrm{0}}…

Question Number 33258 by prof Abdo imad last updated on 14/Apr/18 $$if\frac{1}{1+cosx}=\frac{a_0}{2}+\sum _{n⩾1}{a}_{n}cos\left(nx\right)calculate{a}_0$$$$and{a}_n$$ Terms of Service Privacy Policy Contact:…

Question Number 33257 by prof Abdo imad last updated on 14/Apr/18 $$letg\left(x\right)=\frac{1}{1+x^4}$$$$1)find{g}^{\left(n\right)}\left(x\right)$$$$2)calculate{g}^{\left(n\right)}\left(0\right)$$$$3)ifg\left(x\right)=\mathrm{\Sigma }{u}_n{x}^{n}findthesequence{u}_n$$…

Question Number 33232 by prof Abdo imad last updated on 13/Apr/18 $$findthevalueof{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{xsin\left(2x\right)}{{(1+4x^2)}^2}dx.$$ Commented by prof Abdo imad last updated…