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	$$ \displaystyle\int \dfrac{\cos\left(4x\right)}{\sin\left(2x\right){\cdot}\cos\left(2x\right)}\, \mathrm d x $$	628
2	$$ $$	149
3	$$ \displaystyle\int {x}^{2}+3x-1\, \mathrm d x $$	74
4	$$ \displaystyle\int \dfrac{1}{1+{x}^{4}}\, \mathrm d x $$	57
5	$$ $$	29
6	$$ \displaystyle\int 2{\cdot}\cot\left(4x\right)\, \mathrm d x $$	23
7	$$ $$	21
8	$$ \displaystyle\int^{\pi/3}_{\pi/6} \dfsqrtac{\cos\left(4x\sqrtight)}{\sin\left(2x\sqrtight){\cdot}\cos\left(2x\sqrtight)}\, \mathsqrtm d x $$	21
9	$$ \displaystyle\int {x}^{2}{\cdot}\sin\left(x\right)\, \mathrm d x $$	19
10	$$ \displaystyle\int+\dfrac{1}{1+{x}^{4}}\,+\mathrm+d+x $$	18
11	$$ \displaystyle\int^{1}_{0} \dfrac{1}{1+{x}^{6}}\, \mathrm d x $$	18
12	$$ \displaystyle\int {x}^{2}\, \mathrm d x $$	17
13	$$ \displaystyle\int^{1}_{0} {x}^{2}+1\, \mathrm d x $$	17
14	$$ \displaystyle\int \cos\left(x\right)\, \mathrm d x $$	17
15	$$ \displaystyle\int^{\pi}_{0} \sin\left(x\right)\, \mathrm d x $$	17
16	$$ $$	16
17	$$ $$	16
18	$$ \displaystyle\int^{\pi/4}_{0} \sin\left(x\right)\, \mathrm d x $$	14
19	$$ $$	14
20	$$ \displaystyle\int^{e}_{1} x{\cdot}\ln\left(x\right)\, \mathrm d x $$	14
21	$$ \displaystyle\int^{\pi/2}_{0} \sin\left(x\right)\, \mathrm d x $$	13
22	$$ $$	13
23	$$ \displaystyle\int \tan\left(x\right)\, \mathrm d x $$	13
24	$$ $$	13
25	$$ $$	12
26	$$ $$	12
27	$$ $$	11
28	$$ \displaystyle\int {\left(\cos\left(x\right)\right)}^{2}\, \mathrm d x $$	11
29	$$ \displaystyle\int \dfrac{1}{x}\, \mathrm d x $$	11
30	$$ $$	11
31	$$ $$	11
32	$$ $$	10
33	$$ $$	10
34	$$ $$	10
35	$$ \displaystyle\int \dfrac{1}{{x}^{2}}\, \mathrm d x $$	10
36	$$ \displaystyle\int^{\infty}_{0} 2x{\cdot}{\mathrm{e}}^{-2x}\, \mathrm d x $$	10
37	$$ $$	10
38	$$ \displaystyle\int \sin\left(x\right)\, \mathrm d x $$	10
39	$$ \displaystyle\int \sqrt{\dfrac{{\mathrm{e}}^{x}}{2-{\mathrm{e}}^{x}}}\, \mathrm d x $$	10
40	$$ \displaystyle\int \dfrac{1}{{\mathrm{e}}^{2}}\, \mathrm d x $$	9
41	$$ $$	9
42	$$ $$	9
43	$$ \displaystyle\int^{3}_{0} \dfrac{18}{7-4x}+\dfrac{5x}{7-4x}\, \mathrm d x $$	9
44	$$ \displaystyle\int^{6}_{0} 2x-{x}^{2}+4x\, \mathrm d x $$	9
45	$$ \displaystyle\int \dfrac{2}{{x}^{3}}\, \mathrm d x $$	9
46	$$ $$	9
47	$$ \displaystyle\int^{10}_{0} 150-0.5x\, \mathrm d x $$	9
48	$$ $$	9
49	$$ $$	8
50	$$ $$	8