Category: Integration

Question Number 97794 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}+\mathrm{y}=\frac{1}{\mathrm{cosx}}$$ Commented by john santu last updated on 10/Jun/20 $${\mathrm{y}}^{″}+{\mathrm{y}}^{\prime }=\sec \mathrm{x}$$$$\mathrm{homogenous}\:\mathrm{solution}\: \…

Question Number 97782 by 175 last updated on 09/Jun/20 $$Evaluate:$$$$\int \frac{sinx}{1+{sin}^{2}x}dx$$ Commented by mr W last updated on 09/Jun/20 $$=−\int\frac{{d}\left(\mathrm{cos}\:{x}\right)}{\left(\sqrt{\mathrm{2}}−\mathrm{cos}\:{x}\right)\left(\sqrt{\mathrm{2}}+\mathrm{cos}\:{x}\right)} \…

Question Number 32206 by Glorious Man last updated on 21/Mar/18 $$\mathrm{Find}\underset{\mathrm{k}=1}{\sum ^{\mathrm{\infty }}}\left(\underset{\mathrm{k}-1}{\stackrel{\mathrm{k}}{\int }}{\mathrm{x}}^{-\mathrm{x}}\mathrm{dx}\right).$$$$$$ Terms of Service Privacy Policy…

Question Number 97707 by Power last updated on 09/Jun/20 Answered by smridha last updated on 09/Jun/20 $$=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{e}}^{\boldsymbol{{ix}}} }{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }\boldsymbol{{dx}}\:+\frac{\mathrm{1}}{\mathrm{2}}\int_{+\infty} ^{−\infty} \frac{\boldsymbol{{e}}^{−\left(−\boldsymbol{{ix}}\right)} }{\left(−\boldsymbol{{x}}\right)^{\mathrm{2}}…

Question Number 163212 by smallEinstein last updated on 04/Jan/22 Commented by mr W last updated on 05/Jan/22 $$whatapity,MrEinstein!ihaveasked$$$$youformoretimestocroptheimage$$$$properlywhenyouarepostingit.$$$${but}\:{you}\:{ignored}\:{my}\:{suggestion}\:{and} \…