Category: Integration

Question Number 151064 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}::{\int }_0^{\pi }\arctan \left(\frac{2\sin {}^2\mathrm{x}}{1-2\sqrt{2}\phi \cos \mathrm{x}+2{\phi }^2}\right)\mathrm{dx}=\pi \arctan \sqrt{\phi }(\phi =\frac{\sqrt{5}-1}{2})$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 151066 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}::{\int }_0^{\pi /2}(\arctan \left(\frac{\sin \mathrm{x}}{2}\right)+\arctan \left(\frac{\cos 3\mathrm{x}+15\cos \mathrm{x}}{8}\right))\mathrm{dx}$$$$=\frac{{\pi }^2}{4}-{\ln }^2(1+\sqrt{2})$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 151063 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}::{\int }_0^{\mathrm{\infty }}\frac{\ln (1+\mathrm{x})}{({\pi }^2+{\ln }^2\mathrm{x})\mathrm{x}}\mathrm{dx}=\gamma$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 151053 by Tawa11 last updated on 17/Aug/21 Answered by puissant last updated on 18/Aug/21 $$Q={\int }_0^1\frac{sin\left(lnx\right)-ln\left(x\right)}{{ln}^{2}x}dx$$$${t}=−{lnx}\:\rightarrow\:{x}={e}^{−{t}} \rightarrow{dx}=−{e}^{−{t}} {dt} \…

Question Number 85488 by john santu last updated on 22/Mar/20 $$\int \frac{dx}{{(x^4+x^2+1)}^{\frac{3}{4}}}$$ Answered by MJS last updated on 22/Mar/20 $$\mathrm{trying}\:\mathrm{around}\:\mathrm{I}\:\mathrm{landed}\:\mathrm{on} \…