Questions
The value of is
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a
3x+3(x3)−6(x6)+6log(x6+1)+C
b
2x+6x6−6log(x6+1)+C
c
2x−3(x3)+6(x6)−6log(x6+1)+C
d
none of these
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Correct option is C
We want a substitution that will allow us to find both the square root and the cube root without getting fractional exponents. Thus we want a substitution of the form x=uk where k is a multiple of 2 and 3. Let us use theleast common multiple 6.Let x=u6,dx=6u5du∫dxx+x3=∫6u5duu3+u2=6∫u3u+1du=6∫u2−u+1−1u+1du=2u3−3u2+6u−6log(u+1)+C=2x−3(x3)+6(x6)−6log(x6+1)+CSimilar Questions
is equal to
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