Category: Integration

Question Number 7959 by tawakalitu last updated on 25/Sep/16 $$\int \frac{{sin}^{-1}\left(x\right)}{1-x^2}dx$$ Commented by nick last updated on 26/Sep/16 $${do}\:{you}\:{mean}\:\int\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \…

Question Number 73489 by abdomathmax last updated on 13/Nov/19 $$calculate{\int }_0^{\mathrm{\infty }}\frac{arctan(3+x^2)}{{(2x^2+9)}^2}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 73483 by abdomathmax last updated on 13/Nov/19 $$find\int \frac{dx}{x+2-\sqrt{x^2-x+7}}$$ Answered by MJS last updated on 13/Nov/19 $$\int \frac{dx}{x+2-\sqrt{x^2-x+7}}=\int \frac{dx}{x+2-\sqrt{{(x-\frac{1}{2})}^2+\frac{27}{4}}}=$$$$\:\:\:\:\:\left[{t}=\frac{\sqrt{\mathrm{3}}}{\mathrm{9}}\left(\mathrm{2}{x}−\mathrm{1}\right)\:\rightarrow\:{dx}=\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}{dt}\right]…

Question Number 73480 by abdomathmax last updated on 13/Nov/19 $$find{\int }_0^{\mathrm{\infty }}{xe}^{-x^2}arcran(x+\frac{1}{x})dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 73479 by abdomathmax last updated on 13/Nov/19 $$find\int \frac{3x+2}{{(x+1)}^2{(x-2)}^3}dx$$ Commented by abdomathmax last updated on 17/Nov/19 $${let}\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{3}{x}+\mathrm{2}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} } \…