Integrals

(the database of solved problems)

All the problems and solutions shown below were generated using the Integral Calculator.

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ID	Problem	Count
1	$$ \displaystyle\int \dfrac{\cos\left(4x\right)}{\sin\left(2x\right){\cdot}\cos\left(2x\right)}\, \mathrm d x $$	413
2	$$ \displaystyle\int {x}^{2}+3x-1\, \mathrm d x $$	24
3	$$ \displaystyle\int^{1}_{0} \dfrac{1}{1+{x}^{6}}\, \mathrm d x $$	18
4	$$ \displaystyle\int \dfrac{1}{1+{x}^{4}}\, \mathrm d x $$	15
5	$$ $$	11
6	$$ \displaystyle\int^{10}_{0} 150-0.5x\, \mathrm d x $$	9
7	$$ \displaystyle\int {x}^{2}{\cdot}\sin\left(x\right)\, \mathrm d x $$	8
8	$$ \displaystyle\int \dfrac{1}{x}\, \mathrm d x $$	8
9	$$ \displaystyle\int^{30}_{0} \dfrac{2000{\cdot}30}{150-0.5x}\, \mathrm d x $$	7
10	$$ \displaystyle\int^{1}_{0} \sin\left({x}^{2}\right)\, \mathrm d x $$	6
11	$$ \displaystyle\int^{\infty}_{0} \dfrac{{x}^{3}}{{\mathrm{e}}^{x}-1}\, \mathrm d x $$	6
12	$$ \displaystyle\int {x}^{2}{\cdot}\sqrt{3+2{x}^{2}}\, \mathrm d x $$	6
13	$$ \displaystyle\int^{1}_{0} {x}^{2}+1\, \mathrm d x $$	6
14	$$ \displaystyle\int \dfrac{1}{{x}^{3}+1}\, \mathrm d x $$	5
15	$$ \displaystyle\int \tan\left(x\right)\, \mathrm d x $$	5
16	$$ \displaystyle\int {x}^{2}\, \mathrm d x $$	5
17	$$ \displaystyle\int^{\pi/2}_{0} \sqrt{\sin\left(x\right)}{\cdot}{\left(\cos\left(x\right)\right)}^{5}\, \mathrm d x $$	5
18	$$ \displaystyle\int \dfrac{x{\cdot}\cos\left(2\right){\cdot}{x}^{2}}{\sqrt{1}}-4{x}^{4}\, \mathrm d x $$	5
19	$$ \displaystyle\int^{1}_{0} {\mathrm{e}}^{{x}^{2}}\, \mathrm d x $$	5
20	$$ \displaystyle\int 3x+2\, \mathrm d x $$	5
21	$$ \displaystyle\int 150-0.5x\, \mathrm d x $$	5
22	$$ \displaystyle\int 2{\cdot}\cot\left(4x\right)\, \mathrm d x $$	5
23	$$ $$	5
24	$$ \displaystyle\int 6x{\cdot}{\left(3+x\right)}^{-2}\, \mathrm d x $$	5
25	$$ \displaystyle\int \dfrac{1}{{\left(\cos\left(x\right)\right)}^{2}}\, \mathrm d x $$	5
26	$$ \displaystyle\int \dfrac{1}{x}-\color{orangered}{\square}\, \mathrm d x $$	5
27	$$ \displaystyle\int x{\cdot}\sin\left(3{x}^{2}+{\pi}\right)\, \mathrm d x $$	4
28	$$ \displaystyle\int {x}^{2}{\cdot}\sqrt{x}\, \mathrm d x $$	4
29	$$ \displaystyle\int^{\pi/2}_{-\pi/2} 2{\cdot}\csc\left(x\right)-\csc\left(x\right)\, \mathrm d x $$	4
30	$$ \displaystyle\int \mathrm{e}^{2x}\, \mathrm d x $$	4
31	$$ \displaystyle\int \mathrm{e}^{2x}{\cdot}\cos\left(3x\right)\, \mathrm d x $$	4
32	$$ \displaystyle\int {x}^{-1}\, \mathrm d x $$	4
33	$$ $$	4
34	$$ \displaystyle\int \sqrt{1-{x}^{2}}\, \mathrm d x $$	4
35	$$ \displaystyle\int^{3}_{-1} \dfrac{14-6{x}^{2}}{4}\, \mathrm d x $$	4
36	$$ \displaystyle\int^{8.682}_{0} {\left(-\sqrt{\dfrac{x}{10}}-\sin\left(0.5x\right)\right)}^{2}\, \mathrm d x $$	4
37	$$ $$	4
38	$$ \displaystyle\int^{3\pi/2}_{\pi} \left(2x-3\right){\cdot}\sin\left(2x\right)\, \mathrm d x $$	4
39	$$ \displaystyle\int \sqrt{{\left(\dfrac{3}{2}\right)}^{2}-{\left(x-\dfrac{5}{2}\right)}^{2}}\, \mathrm d x $$	4
40	$$ \displaystyle\int \dfrac{1}{\sqrt{4{x}^{2}+9}}\, \mathrm d x $$	4
41	$$ \displaystyle\int {x}^{\frac{2}{5}}\, \mathrm d x $$	4
42	$$ $$	4
43	$$ \displaystyle\int \sinh\left(3x+9\right){\cdot}x\, \mathrm d x $$	4
44	$$ $$	4
45	$$ \displaystyle\int \dfrac{{x}^{3}}{{\mathrm{e}}^{x}-1}\, \mathrm d x $$	4
46	$$ \displaystyle\int^{2\pi}_{0} x{\cdot}\sin\left(x\right)\, \mathrm d x $$	4
47	$$ $$	4
48	$$ \displaystyle\int \csc\left(x\right)\, \mathrm d x $$	4
49	$$ \displaystyle\int^{2}_{1} \left(x-2\right){\cdot}\ln\left(x\right)-{x}^{2}+3x-2\, \mathrm d x $$	4
50	$$ \displaystyle\int^{5}_{-5} \dfrac{1}{x}\, \mathrm d x $$	4