Find the indefinite integral of the following function and check the result by differentiation. $$\int \frac { 6 s ^ { 5 } } { s ^ { 6 } + 4 } d s$$
A) $\frac { 1 } { 2 } \sqrt { s ^ { 6 } + 4 } + C$
B) $\sqrt { s ^ { 6 } + 4 } + C$
C) $2 \sqrt { s ^ { 5 } + 4 } + C$
D) $2 \sqrt { s ^ { 6 } + 4 } + C$
E) $\frac { 1 } { 2 } \sqrt { s ^ { 5 } + 4 } + C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = s^6 + 4 $, then $ du = 6s^5 ds $. The integral becomes $\int \frac{1}{\sqrt{u}} du$, which evaluates to $2\sqrt{u} + C$. Substituting back, we get $2\sqrt{s^6 + 4} + C$.

Find the Indefinite Integral of the Following Function and Check ∫6s5s6+4ds\int \frac { 6 s ^ { 5 } } { s ^ { 6 } + 4 } d s∫s6+46s5​ds

Find the Indefinite Integral of the Following Function and Check $\int \frac { 6 s ^ { 5 } } { s ^ { 6 } + 4 } d s$