Category: Integration

Question Number 66728 by Tony Lin last updated on 19/Aug/19 $${\int }_1^{\mathrm{\infty }}\frac{1}{x\sqrt{x^2+1}}=?$$ Commented by mathmax by abdo last updated on 19/Aug/19…

Question Number 132235 by bemath last updated on 12/Feb/21 $$\mathrm{I}=\int \frac{3\mathrm{x}+5}{{({\mathrm{x}}^2+2\mathrm{x}+3)}^2}\mathrm{dx}?$$ Answered by bemath last updated on 12/Feb/21 Commented by bemath last…

Question Number 66694 by mathmax by abdo last updated on 18/Aug/19 $$letf\left(a\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dx}{(x^4+x^2+a)}witha\in ]\frac{1}{4},+\mathrm{\infty }[$$$$1)calculatef\left(a\right)$$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} }…

Question Number 132192 by benjo_mathlover last updated on 12/Feb/21 $$\int \frac{\mathrm{dx}}{\csc \mathrm{x}+\sec \mathrm{x}}$$ Answered by Dwaipayan Shikari last updated on 12/Feb/21 $$\int \frac{sinxcosx}{sinx+cosx}dx$$$$=\frac{1}{2}\int sinx+cosx-\frac{1}{sinx+cosx}dx$$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({sinx}−{cosx}\right)−\int\frac{{dt}}{\mathrm{1}−{t}^{\mathrm{2}}…

Question Number 132191 by rs4089 last updated on 12/Feb/21 $${\int }_0^1\frac{{log}_e(x+1)}{x(x^2+1)}dx$$ Answered by mathmax by abdo last updated on 12/Feb/21…