For comparison with other CAS choose from: Axiom Derive Macsyma Maple Reduce
Integrate[ x ^2 (a+b x)^p, x]
3
p 2 a
(a + b x) (-------------------------- -
3
b (1 + p) (2 + p) (3 + p)
2
2 a p x
----------------------------- +
(3 + p) (b + b p) (2 b + b p)
2 3
a p x b x
------------------- + ---------)
(3 + p) (2 b + b p) 3 b + b p
Simplify[%]
1 + p 2 2 2
((a + b x) (2 a - 2 a b x - 2 a b p x + 2 b x +
2 2 2 2 2 3 2 3
3 b p x + b p x )) / (b (6 + 11 p + 6 p + p ))
Integrate[ x^2 Log[x^2 + a^2], x]
3 x
2 3 2 a ArcTan[-] 3 2 2
2 a x 2 x a x Log[a + x ]
------ - ---- - -------------- + ---------------
3 9 3 3
Simplify[%]
2 3 3 x 3 2 2
6 a x - 2 x - 6 a ArcTan[-] + 3 x Log[a + x ]
a
--------------------------------------------------
9
Simplify[Integrate[ x d^x Sin[x], x ]]
x 2
(d (-(x Cos[x]) + 2 Cos[x] Log[d] - x Cos[x] Log[d] +
2
Sin[x] + x Log[d] Sin[x] - Log[d] Sin[x] +
3 2 2
x Log[d] Sin[x])) / (1 + Log[d] )
Simplify[Integrate[ x Sqrt[a + b x]^p, x]]
1 + p/2
2 (a + b x) (-2 a + 2 b x + b p x)
-----------------------------------------
2
b (2 + p) (4 + p)
Simplify[
Integrate[ 2x Exp[x^2] Log[x]+ Exp[x^2]/x +
(Log[x]-2)/(Log[x]^2+x)^2 +
((2/x) Log[x]+ (1/x)+1)/ (Log[x]^2+x), x ]]
2
x Log[x] 2
E Log[x] - ----------- + Log[x + Log[x] ]
2
x + Log[x]