RUBI 4.1 results for Charlwood’s integrals

(*requires Rubi package loaded*)

1

Int[ArcSin[x] Log[x], x]

2

Int[((x ArcSin[x])/(Sqrt[1-(x^2)])),x]

3

Int[ArcSin[(Sqrt[x+1])-(Sqrt[x])],x]

4

Int[Log[1+x(Sqrt[1+(x^2)])],x]

5

Int[(((Cos[x])^2)/(Sqrt[((Cos[x])^4)+((Cos[x])^2)+1])),x]

6

Int[Tan[x](Sqrt[1+((Tan[x])^4)]),x]

7

Int[((Tan[x])/(Sqrt[((Sec[x])^3)+1])),x]

8

Int[(Sqrt[((Tan[x])^2)+2Tan[x]+2]),x]

9

Int[Sin[x]ArcTan[(Sqrt[Sec[x]-1])],x]

10

Int[(((x^3)Exp[ArcSin[x]])/(Sqrt[1-(x^2)])),x]

Int[((Sec[x])/(Sqrt[1+Sin[x]])), x]

11

Int[(x*Log[1+x^2]*Log[x+Sqrt[1+x^2]])/Sqrt[1+x^2],x]

12

Int[ArcTan[x+Sqrt[1-x^2]],x]

13

Int[x*ArcTan[x+Sqrt[1-x^2]]/Sqrt[1-x^2],x]

14

Int[ArcSin[x]/(1+Sqrt[1-x^2]),x]

15

Int[Log[x+Sqrt[1+x^2]]/(1-x^2)^(3/2),x]

16

Int[ArcSin[x]/(1+x^2)^(3/2),x]

17

Int[Log[x+Sqrt[x^2-1]]/(1+x^2)^(3/2),x]

18

Int[Log[x]/(x^2*Sqrt[x^2-1]),x]

19

Int[Sqrt[1+x^3]/x,x]

20

Int[x*Log[x+Sqrt[x^2-1]]/Sqrt[x^2-1],x]