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Category: Integration

let-give-f-x-0-1-ln-1-x-2-t-2-t-2-dt-with-x-lt-1-by-using-derivation-under-find-the-value-of-f-x-

Question Number 28819 by abdo imad last updated on 30/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${by}\:{using}\:{derivation}\:{under}\:\int\:\:{find}\:{the}\:{value}\:{of}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy Policy…

1-cot-2-x-1-sin-x-dx-

Question Number 159870 by tounghoungko last updated on 21/Nov/21 $$\:\:\int\:\frac{\mathrm{1}−\mathrm{cot}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 21/Nov/21 $${I}=\int\frac{\mathrm{1}−\mathrm{cot}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}{x}}{dx}=\int\frac{\left(\mathrm{1}−\mathrm{cot}^{\mathrm{2}} {x}\right)\left(\mathrm{1}−\mathrm{sin}{x}\right)}{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} {x}}{dx}…