Category: Integration

Question Number 183450 by cortano1 last updated on 26/Dec/22 $$\underset{0}{\stackrel{x^2}{\int }}f(2t^3-t^2-6)dt=\ln x$$$$thenf\left(106\right)=?$$ Answered by mahdipoor last updated on…

Question Number 52363 by Necxx last updated on 06/Jan/19 $$integrate\frac{{\sin }^{2}x{\cos }^{2}x}{{sin}^{3}x+{cos}^{3}x}dx$$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jan/19 $$=\left(−\mathrm{1}\right)\int\frac{\mathrm{1}−{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}}…

Question Number 183382 by mathlove last updated on 25/Dec/22 Commented by CElcedricjunior last updated on 25/Dec/22 $$\int \frac{\mathit{x}+1}{2{\mathit{x}}^2+6\mathit{x}+9}\mathit{d}\mathit{x}=\frac{1}{4}\int \frac{4\mathit{x}+6}{2{\mathit{x}}^2+6\mathit{x}+9}\mathit{d}\mathit{x}-\frac{1}{4}\int \frac{-2}{2{\mathit{x}}^2+6\mathit{x}+9}\mathit{d}\mathit{x}$$$$=\frac{\mathrm{1}}{\mathrm{4}}\boldsymbol{{ln}}\mid\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{{x}}+\mathrm{9}\mid−\frac{\mathrm{1}}{\mathrm{4}}\int\frac{{dx}}{\left(\boldsymbol{{x}}+\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{9}}{\mathrm{4}}}\:\boldsymbol{{t}}=\frac{\mathrm{2}\boldsymbol{{x}}+\mathrm{3}}{\mathrm{3}} \…

Question Number 117817 by peter frank last updated on 13/Oct/20 Commented by Lordose last updated on 13/Oct/20 $$\mathrm{A}=\int {\mathrm{a}}^{\sqrt{\mathrm{x}}}\mathrm{dx}$$$$\mathrm{u}=\sqrt{\mathrm{x}}\Rightarrow \mathrm{dx}=2\mathrm{udu}$$$$\mathrm{A}\:=\int\mathrm{2ua}^{\mathrm{u}} \mathrm{du} \…

Question Number 117806 by mnjuly1970 last updated on 13/Oct/20 $$\dots nicecalculus\dots$$$$i::1+\frac{4}{9}+\frac{9}{36}+\frac{16}{100}+\dots =??$$$$ii::{\int }_0^{\frac{\pi }{2}}{x}^{2}cot\left(x\right)dx=??$$$$m.n.1970$$$$$$ Commented by…