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Category: Integration

0-1-sin-x-1-cos-x-dx-

Question Number 186193 by normans last updated on 02/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{\boldsymbol{{sin}}\:\left(\boldsymbol{{x}}\right)}{\mathrm{1}\:\:+\:\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)}\:\:\boldsymbol{{dx}} \\ $$ Answered by CElcedricjunior last updated on 02/Feb/23 $$\int_{\mathrm{0}} ^{\mathrm{1}}…

2-4-2x-2-1-1-x-2-2-dx-

Question Number 186194 by normans last updated on 02/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{1}\:+\:\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} }\:\:−\:\:\mathrm{2}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$ Commented by MJS_new last updated…

1-2-1-2-x-2-x-x-2-2-dx-

Question Number 186195 by normans last updated on 02/Feb/23 $$ \\ $$$$\:\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\:\frac{\mathrm{1}/\mathrm{2}\:\centerdot\left(\boldsymbol{{x}}^{\mathrm{2}} \right)\:}{\boldsymbol{{x}}\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\:\mathrm{2}}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$ Answered by MJS_new last updated on 02/Feb/23…

My-old-problem-0-tan-1-1-cos-x-x-2-dx-

Question Number 186190 by normans last updated on 02/Feb/23 $$ \\ $$$$\:\:\:\:\boldsymbol{{My}}\:\boldsymbol{{old}}\:\boldsymbol{{problem}}.. \\ $$$$\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{+\infty} {\int}}\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{1}−\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\right)}{\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}}\:\:\: \\ $$$$ \\ $$ Commented by MJS_new…

0-pi-1-cos-2-x-dx-

Question Number 186181 by cortano1 last updated on 02/Feb/23 $$\:\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 02/Feb/23 $$\int\sqrt{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \:{x}}\:{dx}=\int\sqrt{\mathrm{2}−\mathrm{sin}^{\mathrm{2}} \:{x}}\:{dx}=…

2-2-tan-1-2-cos-x-2-x-2-dx-

Question Number 186170 by normans last updated on 01/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\:\:\:\frac{\boldsymbol{{tan}}^{−\mathrm{1}} \:\left(\:\mathrm{2}\:−\:\boldsymbol{{cos}}\:\left(\boldsymbol{{x}}\right)\right)\:\:\:\:}{\mathrm{2}\:+\:\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}} \\ $$$$ \\ $$ Answered by MJS_new last updated…

so-easy-cos-2-4x-sin-4-2x-dx-

Question Number 186171 by normans last updated on 01/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{so}}\:\boldsymbol{{easy}}\right] \\ $$$$\:\:\:\:\:\:\:\int\:\boldsymbol{{cos}}^{\mathrm{2}} \:\left(\mathrm{4}\boldsymbol{{x}}\right)\:+\:\boldsymbol{{sin}}^{\mathrm{4}} \:\left(\mathrm{2}\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}\:\:\: \\ $$$$ \\ $$ Answered by MJS_new last updated…

I-2-cos-2-x-1-1-sin-x-tan-x-dx-

Question Number 186152 by normans last updated on 01/Feb/23 $$ \\ $$$$\:\:\:\boldsymbol{{I}}=\:\:\underset{\mathrm{2}} {\overset{\boldsymbol{\pi}} {\int}}\:\:\:\frac{\boldsymbol{{cos}}^{\mathrm{2}} \:\left(\boldsymbol{{x}}\right)\:−\:\mathrm{1}\:}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\left(\boldsymbol{{x}}\right)\:−\:\boldsymbol{{tan}}\:\left(\boldsymbol{{x}}\right)}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$ Answered by MJS_new last updated on…