Category: Integration

Question Number 155919 by horpy4 last updated on 05/Oct/21 Answered by physicstutes last updated on 05/Oct/21 $$\mathbf{F}\times \mathbf{V}=\left|\begin{array}{ccc}i& j& k\\ 3u& u^2& u+2\\ 2u& -3u& u-2\end{array}\right|=i(u^3-2u^2+3u^2-6u)$$$$−\:{j}\left(\mathrm{3}{u}^{\mathrm{2}} −\mathrm{6}{u}−\mathrm{2}{u}^{\mathrm{2}} −\mathrm{4}{u}\right)\:+\:{k}\left(−\mathrm{9}{u}^{\mathrm{2}}…

Question Number 155897 by cortano last updated on 05/Oct/21 $$\int \mathrm{x}{\left(\arctan \mathrm{x}\right)}^2\mathrm{dx}=?$$ Answered by puissant last updated on 05/Oct/21 $$Q=\int x{\left(arctanx\right)}^{2}dx..$$$${IBP}\:\:\Rightarrow\:.. \…

Question Number 24817 by A1B1C1D1 last updated on 26/Nov/17 Answered by mrW1 last updated on 26/Nov/17 $$={\int }_0^4[\frac{1}{2}(y-\frac{y^2}{16})+y(\sqrt{y}-\frac{y}{4})]dy$$$$=\int_{\mathrm{0}} ^{\:\mathrm{4}} \left(\frac{{y}}{\mathrm{2}}−\frac{\mathrm{9}{y}^{\mathrm{2}} }{\mathrm{32}}+{y}^{\frac{\mathrm{3}}{\mathrm{2}}}…

Question Number 155883 by john_santu last updated on 05/Oct/21 $$\int \frac{\tan {}^{2}x}{1-\tan {}^{2}x}dx=?$$ Commented by aliyn last updated on 05/Oct/21 $$\boldsymbol{{I}}\:=\:\int\:\frac{\boldsymbol{{tan}}^{\mathrm{2}} \boldsymbol{{x}}}{\mathrm{1}\:−\:\boldsymbol{{tan}}^{\mathrm{2}} \boldsymbol{{x}}}\:\boldsymbol{{dx}} \…

Question Number 90321 by M±th+et£s last updated on 22/Apr/20 $$\int \frac{1}{x\sqrt[3]{1+x^5}}dx$$$$$$$$\int \frac{1}{{sin}^2\left(x\right)+5sin\left(x\right)+6}dx$$$$$$$$\int \frac{2z-5}{4z^2+4z+5}dz$$$$$$$$\int{sec}^{\mathrm{5}}…