Integrals
(the database of solved problems)
All the problems and solutions shown below were generated using the Integral Calculator.
| ID |
Problem |
Count |
| 6001 | $$ $$ | 1 |
| 6002 | $$ $$ | 1 |
| 6003 | $$ $$ | 1 |
| 6004 | $$ $$ | 1 |
| 6005 | $$ $$ | 1 |
| 6006 | $$ \int^{\pi}_{0} {2}\sqrt{{{2}-{\cos{{\left({x}\right)}}}}}^{{2}}+{\left({2}{\sin{{\left({x}\right)}}}\right)}^{{2}} \, d\,x $$ | 1 |
| 6007 | $$ \displaystyle\int^{\pi/2}_{0} \dfrac{\sin\left(x\right)}{\sin\left(x\right)+\cos\left(x\right)}\, \mathrm d x $$ | 1 |
| 6008 | $$ \displaystyle\int^{\pi}_{0} \dfrac{{x}^{2}{\cdot}\sin\left(x\right)}{3+\cos\left(2x\right)}\, \mathrm d x $$ | 1 |
| 6009 | $$ \displaystyle\int^{0}_{\pi} \dfrac{{x}^{2}{\cdot}\sin\left(x\right)}{3+\cos\left(2x\right)}\, \mathrm d x $$ | 1 |
| 6010 | $$ \displaystyle\int \dfrac{{\left(\sin\left(x\right)\right)}^{2}}{2}\, \mathrm d x $$ | 1 |
| 6011 | $$ \displaystyle\int \dfrac{{\left({\mathrm{e}}^{x}+1\right)}^{2}}{{\mathrm{e}}^{x}}\, \mathrm d x $$ | 1 |
| 6012 | $$ \displaystyle\int \sin\left(x\sqrtight){\cdot}\cos\left({x}^{3}\sqrtight)\, \mathsqrtm d x $$ | 1 |
| 6013 | $$ \int^{0}_{\pi} {2}\sqrt{{{2}{\cos{{\left({x}\right)}}}}}^{{2}}+\sqrt{{{2}{\sin{{\left({\left({x}\right)}\right)}}}^{{2}}}} \, d\,x $$ | 1 |
| 6014 | $$ \displaystyle\int \sin\left(\dfrac{{\pi}{\cdot}x}{100}\right){\cdot}\sin\left(\dfrac{{\pi}{\cdot}r}{100}\right){\cdot}x\, \mathrm d x $$ | 1 |
| 6015 | $$ \int^{\pi}_{0} {2}{\cos{{\left({x}\right)}}} \, d\,x $$ | 1 |
| 6016 | $$ \int^{\pi}_{0} {2}\sqrt{{{2}-{\cos{{\left({x}\right)}}}}}^{{2}} \, d\,x $$ | 1 |
| 6017 | $$ \int^{3}_{0} {9}{x}-\frac{{1}}{{3}}{x}^{{3}} \, d\,x $$ | 1 |
| 6018 | $$ $$ | 1 |
| 6019 | $$ \displaystyle\int \dfrac{{x}^{3}-3{x}^{2}+5x-3}{x-1}\, \mathrm d x $$ | 1 |
| 6020 | $$ $$ | 1 |
| 6021 | $$ $$ | 1 |
| 6022 | $$ $$ | 1 |
| 6023 | $$ \displaystyle\int {\left(\sin\left(x\right)\right)}^{2}{\cdot}{\left(\cos\left(x\right)\right)}^{4}\, \mathrm d x $$ | 1 |
| 6024 | $$ \displaystyle\int^{3}_{1} \sqrt{\dfrac{1+9{x}^{4}}{{x}^{3}-1}}\, \mathrm d x $$ | 1 |
| 6025 | $$ \displaystyle\int \dfrac{1}{x}\, \mathrm d x $$ | 1 |
| 6026 | $$ \displaystyle\int \dfrac{\left(1+x\right){\cdot}{\left(1-x\right)}^{1}}{2}\, \mathrm d x $$ | 1 |
| 6027 | $$ $$ | 1 |
| 6028 | $$ \int^{\pi}_{0} {2}\sqrt{{{2}-{\cos{{\left({x}\right)}}}}}^{{2}}+\sqrt{{{2}{\sin{{\left({x}\right)}}}^{{2}}}} \, d\,x $$ | 1 |
| 6029 | $$ \int^{\pi}_{0} {2}\sqrt{{{2}-{\cos{{\left({x}\right)}}}}}^{{2}}+\sqrt{{2}}{\sin{{\left({\left({x}\right)}^{{2}}\right)}}} \, d\,x $$ | 1 |
| 6030 | $$ \int^{\pi}_{0} {2}\sqrt{{{2}-{\cos{{\left({x}\right)}}}}}^{{2}}+\sqrt{{{2}{\sin{{\left({\left({x}\right)}\right)}}}^{{2}}}} \, d\,x $$ | 1 |
| 6031 | $$ \int^{\pi}_{0} {2}{\sin{{\left({x}\right)}}} \, d\,x $$ | 1 |
| 6032 | $$ \int {2}{x}+{3} \, d\,x $$ | 1 |
| 6033 | $$ \displaystyle\int \dfrac{1}{1-\sin\left(x\right)}\, \mathrm d x $$ | 1 |
| 6034 | $$ \displaystyle\int^{1}_{0} x{\cdot}\ln\left(x\right)\, \mathrm d x $$ | 1 |
| 6035 | $$ $$ | 1 |
| 6036 | $$ $$ | 1 |
| 6037 | $$ $$ | 1 |
| 6038 | $$ \int^{3}_{1} {5}{x}+{9} \, d\,x $$ | 1 |
| 6039 | $$ \int^{3}_{1} {5}{x}^{{2}}+{6} \, d\,x $$ | 1 |
| 6040 | $$ \displaystyle\int a{\cdot}\sin\left(cx\right){\cdot}\sin\left(cx\right)\, \mathrm d x $$ | 1 |
| 6041 | $$ \displaystyle\int \sqrt{1+{x}^{2}}\, \mathrm d x $$ | 1 |
| 6042 | $$ \displaystyle\int^{\infty}_{0} \dfrac{1}{\sqrt{{x}^{2}-1}}{\cdot}{\mathrm{e}}^{-x}\, \mathrm d x $$ | 1 |
| 6043 | $$ \displaystyle\int {\left(\cos\left(x\right)\right)}^{2}\, \mathrm d x $$ | 1 |
| 6044 | $$ \displaystyle\int \sqrt{1-{x}^{2}}\, \mathrm d x $$ | 1 |
| 6045 | $$ \displaystyle\int 1-{x}^{2}{\cdot}\tan\left(x\right)\, \mathrm d x $$ | 1 |
| 6046 | $$ \displaystyle\int^{20}_{0} x{\cdot}{\mathrm{e}}^{\frac{-x}{5}}\, \mathrm d x $$ | 1 |
| 6047 | $$ \displaystyle\int^{-2}_{-\infty} \dfrac{1}{{x}^{5}}\, \mathrm d x $$ | 1 |
| 6048 | $$ $$ | 1 |
| 6049 | $$ $$ | 1 |
| 6050 | $$ $$ | 1 |
