Find the most general antiderivative.
-$\int ( \sqrt { t } - \sqrt [ 6 ] { t } ) d t$
A) $\frac { 2 } { 3 } t ^ { 3 / 2 } - \frac { 6 } { 7 } t ^ { 7 / 6 } + C$
B) $\sqrt { t } - \sqrt [ 5 ] { t } + C$
C) $\frac { 3 } { 2 } t ^ { 3 / 2 } - \frac { 7 } { 6 } t ^ { 7 / 6 } + C$
D) $\frac { - 1 } { 2 } t ^ { 1 / 2 } - \frac { 1 } { 6 } t ^ { - 5 / 6 } + C$

Question

Quizplus · Accepted Answer

The antiderivative of $ \sqrt{t} $ is $ \frac{2}{3}t^{3/2} $ and the antiderivative of $ \sqrt[6]{t} $ is $ \frac{6}{7}t^{7/6} $, thus the most general antiderivative is $ \frac{2}{3}t^{3/2} - \frac{6}{7}t^{7/6} + C $.

Find the Most General Antiderivative ∫(t−t6)dt\int ( \sqrt { t } - \sqrt [ 6 ] { t } ) d t∫(t​−6t​)dt

Find the Most General Antiderivative $\int ( \sqrt { t } - \sqrt [ 6 ] { t } ) d t$