Evaluate the integral $\int \left( 3 + x ^ { 3 / 5 } \right) d x$ .
A) $3 x + \frac { 5 } { 8 } x ^ { 8 / 5 } + C$
B) $3 x + \frac { 8 } { 5 } x ^ { 8 / 5 } + C$
C) $\frac { 9 } { 2 } + \frac { 5 } { 8 } x ^ { 8 / 5 } + C$
D) $\frac { 3 } { 5 } x ^ { - 2 / 5 } + C$
E) $\frac { 3 } { 5 } x ^ { 8 /5 } + C$

Question

Quizplus · Accepted Answer

The integral of $3$ with respect to $x$ is $3x$, and the integral of $x^{3/5}$ is $\frac{5}{8}x^{8/5}$ (using the power rule for integration, which states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ for $n \neq -1$). Adding these results gives $3x + \frac{5}{8}x^{8/5} + C$.

Evaluate the Integral ∫(3+x3/5)dx\int \left( 3 + x ^ { 3 / 5 } \right) d x∫(3+x3/5)dx

Evaluate the Integral $\int \left( 3 + x ^ { 3 / 5 } \right) d x$