Integrals – Solved Problems Database
All the problems and solutions shown below were generated using the Integral Calculator.
| ID |
Problem |
Count |
| 1 | $$ \displaystyle\int \dfrac{\cos\left(4x\right)}{\sin\left(2x\right){\cdot}\cos\left(2x\right)}\, \mathrm d x $$ | 389 |
| 2 | $$ $$ | 31 |
| 3 | $$ \displaystyle\int {x}^{2}+3x-1\, \mathrm d x $$ | 22 |
| 4 | $$ \displaystyle\int^{1}_{0} \dfrac{1}{1+{x}^{6}}\, \mathrm d x $$ | 18 |
| 5 | $$ \displaystyle\int \dfrac{1}{1+{x}^{4}}\, \mathrm d x $$ | 15 |
| 6 | $$ \displaystyle\int {x}^{2}{\cdot}\sin\left(x\right)\, \mathrm d x $$ | 8 |
| 7 | $$ $$ | 6 |
| 8 | $$ $$ | 6 |
| 9 | $$ \displaystyle\int^{1}_{0} \sin\left({x}^{2}\right)\, \mathrm d x $$ | 6 |
| 10 | $$ \displaystyle\int \dfrac{1}{{x}^{3}+1}\, \mathrm d x $$ | 5 |
| 11 | $$ \displaystyle\int 2{\cdot}\cot\left(4x\right)\, \mathrm d x $$ | 5 |
| 12 | $$ $$ | 5 |
| 13 | $$ \displaystyle\int \tan\left(x\right)\, \mathrm d x $$ | 5 |
| 14 | $$ \displaystyle\int {x}^{2}\, \mathrm d x $$ | 5 |
| 15 | $$ \displaystyle\int 6x{\cdot}{\left(3+x\right)}^{-2}\, \mathrm d x $$ | 5 |
| 16 | $$ \displaystyle\int^{\pi/2}_{-\pi/2} 2{\cdot}\csc\left(x\right)-\csc\left(x\right)\, \mathrm d x $$ | 4 |
| 17 | $$ \displaystyle\int {x}^{-1}\, \mathrm d x $$ | 4 |
| 18 | $$ $$ | 4 |
| 19 | $$ \displaystyle\int \dfrac{3x}{x}+3\, \mathrm d x $$ | 4 |
| 20 | $$ \displaystyle\int x{\cdot}\sin\left(3{x}^{2}+{\pi}\right)\, \mathrm d x $$ | 4 |
| 21 | $$ $$ | 4 |
| 22 | $$ \displaystyle\int \dfrac{1}{\sqrt{4{x}^{2}+9}}\, \mathrm d x $$ | 4 |
| 23 | $$ \displaystyle\int \dfrac{{\left(1+\sqrt{x}\right)}^{\frac{1}{5}}}{x{x}^{\frac{9}{10}}}\, \mathrm d x $$ | 4 |
| 24 | $$ \displaystyle\int {x}^{2}{\cdot}\sqrt{x}\, \mathrm d x $$ | 4 |
| 25 | $$ \displaystyle\int^{3\pi/2}_{\pi} \left(2x-3\right){\cdot}\sin\left(2x\right)\, \mathrm d x $$ | 4 |
| 26 | $$ $$ | 4 |
| 27 | $$ \displaystyle\int^{8.682}_{0} {\left(-\sqrt{\dfrac{x}{10}}-\sin\left(0.5x\right)\right)}^{2}\, \mathrm d x $$ | 4 |
| 28 | $$ \displaystyle\int \cos\left(\color{orangered}{\square}\right)\, \mathrm d x $$ | 4 |
| 29 | $$ \displaystyle\int \sqrt{{\left(\dfrac{3}{2}\right)}^{2}-{\left(x-\dfrac{5}{2}\right)}^{2}}\, \mathrm d x $$ | 4 |
| 30 | $$ $$ | 4 |
| 31 | $$ \displaystyle\int^{2}_{1} \left(x-2\right){\cdot}\ln\left(x\right)-{x}^{2}+3x-2\, \mathrm d x $$ | 4 |
| 32 | $$ $$ | 4 |
| 33 | $$ \displaystyle\int \mathrm{e}^{2x}{\cdot}\cos\left(3x\right)\, \mathrm d x $$ | 4 |
| 34 | $$ \displaystyle\int^{5}_{-5} \dfrac{1}{x}\, \mathrm d x $$ | 4 |
| 35 | $$ $$ | 4 |
| 36 | $$ $$ | 4 |
| 37 | $$ \displaystyle\int \csc\left(x\right)\, \mathrm d x $$ | 4 |
| 38 | $$ \displaystyle\int {x}^{\frac{2}{5}}\, \mathrm d x $$ | 4 |
| 39 | $$ \displaystyle\int \mathrm{e}^{2x}\, \mathrm d x $$ | 4 |
| 40 | $$ \displaystyle\int^{3}_{-1} \dfrac{14-6{x}^{2}}{4}\, \mathrm d x $$ | 4 |
| 41 | $$ $$ | 3 |
| 42 | $$ \displaystyle\int \dfrac{\cos\left(x\right)}{\sin\left(x\right){\cdot}\left(2+\sin\left(x\right)\right)}\, \mathrm d x $$ | 3 |
| 43 | $$ \displaystyle\int^{e}_{1} x{\cdot}\ln\left(x\right)\, \mathrm d x $$ | 3 |
| 44 | $$ \int {10}{x}^{{3}}-{5}\frac{{x}}{\sqrt{{{x}^{{4}}-{x}^{{2}}+{6}}}} \, d\,x $$ | 3 |
| 45 | $$ \displaystyle\int \sqrt{x{\cdot}\left(4-x\right)}\, \mathrm d x $$ | 3 |
| 46 | $$ \displaystyle\int {\left(1-{x}^{2}\right)}^{c}\, \mathrm d x $$ | 3 |
| 47 | $$ \displaystyle\int 3{x}^{2}+x+1\, \mathrm d x $$ | 3 |
| 48 | $$ \displaystyle\int^{\pi/80}_{0} \dfrac{1}{2}{\cdot}0.0000006{\cdot}{\left(40{\cdot}\mathrm{e}^{-15000t}{\cdot}\sin\left(30000t\right)\right)}^{2}\, \mathrm d x $$ | 3 |
| 49 | $$ \displaystyle\int \cos\left(2x\right){\cdot}\cos\left(2x\right)\, \mathrm d x $$ | 3 |
| 50 | $$ $$ | 3 |
