Answer:
(x^(3/4) + x^(4/3)) dx = (4/7)x^(7/4) + (3/7)x^(7/3) + C
Explanation:
To find the antiderivative of g(x) = x^(3/4) + x^(4/3):
Using the power rule for integration:
1. For the term x^(3/4):
∫ x^(3/4) dx = (4/7)x^(7/4)
2. For the term x^(4/3):
∫ x^(4/3) dx = (3/7)x^(7/3)
Combining the antiderivatives of the two terms:
∫ (x^(3/4) + x^(4/3)) dx = (4/7)x^(7/4) + (3/7)x^(7/3) + C