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Category: Integration

0-2pi-dx-5-3sin-2x-

Question Number 133305 by liberty last updated on 21/Feb/21 02πdx5+3sin2x=? Answered by physicstutes last updated on 21/Feb/21 sett=tanx$$\Rightarrow\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:=\:\frac{\mathrm{2}\:\mathrm{tan}\:{x}}{\mathrm{1}+\:\mathrm{tan}^{\mathrm{2}} {x}}\:\:=\:\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…

dt-1-kt-1-t-2-0-lt-k-lt-1-

Question Number 2212 by Yozzi last updated on 09/Nov/15 dt(1kt)1t2=?0<k<1 Commented by 123456 last updated on 09/Nov/15 $$\frac{\mathrm{ln}\:\left(\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+{k}−{x}\right)−\mathrm{ln}\:\left(\mathrm{1}−{kx}\right)}{\:\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}} \

let-f-x-0-sin-t-2-x-2-t-2-2-dt-with-x-gt-0-1-determine-a-explicit-form-for-f-x-2-find-also-g-x-0-sin-t-2-x-2-t-2-3-dt-3-give-f-n-x-at-form-of-int

Question Number 67744 by mathmax by abdo last updated on 31/Aug/19 letf(x)=0sin(t2)(x2+t2)2dtwithx>01)determineaexplicitformforf(x)$$\left.\mathrm{2}\right)\:{find}\:\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}}…