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integrate(x**2*(a+b*x)**p, x)
3 2 3 3 3 2 2 2 2 2 3 p log(b x + a)
((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a )%e
3 3 3 2 3 3
b p + 6b p + 11b p + 6b
Type: Union(Expression Integer,...)
integrate(x**2*log(x**2+a**2), x)
3 2 2 3 x 3 2
3x log(x + a ) + 6a atan(- -) - 2x + 6a x
a
-------------------------------------------
9
Type: Union(Expression Integer,...)
integrate(x*d**x*sin x, x)
3 2 2
(x log(d) - log(d) + x log(d) + 1)sin(x) - x cos(x)log(d)
+
2cos(x)log(d) - x cos(x)
*
x log(d)
%e
/
4 2
log(d) + 2log(d) + 1
Type: Union(Expression Integer,...)
integrate(x*sqrt(a+b*x)**p, x)
+-------+
2 2 2 2 p log(\|b x + a )
((2b p + 4b )x + 2a b p x - 4a )%e
----------------------------------------------------
2 2 2 2
b p + 6b p + 8b
Type: Union(Expression Integer,...)
integrate(2*x*%e**(x**2)*log(x)+%e**(x**2)/x+(log(x)-2)/(log(x)**2+x)**2+ _
((2/x)*log(x)+(1/x)+1)/(log(x)**2+x), x)
2 2
2 2 x 3 x
(log(x) + x)log(log(x) + x) + %e log(x) + (x %e - 1)log(x)
----------------------------------------------------------------
2
log(x) + x
Type: Union(Expression Integer,...)