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Category: Integration

calculate-0-arctan-x-2-x-2-x-2-a-2-dx-with-a-gt-0-2-find-the-value-of-0-arctan-x-2-x-2-x-2-1-dx-

Question Number 77886 by mathmax by abdo last updated on 11/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{x}^{−\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{x}^{−\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}…

e-sinh-x-cosh-x-dx-

Question Number 77887 by aliesam last updated on 11/Jan/20 $$\int\frac{{e}^{{sinh}\left({x}\right)} }{{cosh}\left({x}\right)}\:{dx} \\ $$ Answered by MJS last updated on 12/Jan/20 $$\int\frac{\mathrm{e}^{\mathrm{sinh}\:{x}} }{\mathrm{cosh}\:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{sinh}\:{x}\:\rightarrow\:{dx}=\frac{\mathrm{1}}{\mathrm{cosh}\:{x}}\right] \\…

What-is-1-3-1-x-4-dx-equal-to-a-232-5-b-116-5-c-116-5-d-232-5-

Question Number 12303 by Gaurav3651 last updated on 18/Apr/17 $${What}\:{is}\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\mid\mathrm{1}−{x}^{\mathrm{4}} \:\mid{dx}\:{equal}\:{to}? \\ $$$$\left({a}\right)\:\:−\mathrm{232}/\mathrm{5} \\ $$$$\left({b}\right)\:\:−\mathrm{116}/\mathrm{5} \\ $$$$\left({c}\right)\:\:\:\mathrm{116}/\mathrm{5} \\ $$$$\left({d}\right)\:\:\:\mathrm{232}/\mathrm{5} \\ $$ Answered by…

Let-f-x-be-a-function-such-that-f-1-x-x-3-f-x-0-What-is-1-1-f-x-dx-equal-to-a-2f-1-b-0-c-2f-1-d-4f-1-

Question Number 12302 by Gaurav3651 last updated on 18/Apr/17 $${Let}\:{f}\left({x}\right)\:{be}\:{a}\:{function}\:{such}\:{that} \\ $$$${f}'\left(\mathrm{1}/{x}\right)+{x}^{\mathrm{3}} {f}'\left({x}\right)=\mathrm{0}. \\ $$$${What}\:{is}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}\:{equal}\:{to}? \\ $$$$\left({a}\right)\:\:\mathrm{2}{f}\left(\mathrm{1}\right) \\ $$$$\left({b}\right)\:\:\mathrm{0} \\ $$$$\left({c}\right)\:\:\mathrm{2}{f}\left(−\mathrm{1}\right) \\ $$$$\left({d}\right)\:\:\mathrm{4}{f}\left(\mathrm{1}\right)…