Find the indefinite integral.
$\int \frac { 2 x ^ { 7 } - 5 x ^ { 4 } + 2 } { x ^ { 7 } } d x$
A) $2 x + \frac { 5 } { 4 x ^ { 4 } } - \frac { 1 } { 4 x ^ { 8 } } + C$
B) $2 x + \frac { 5 } { 2 } x ^ { 2 } - \frac { 1 } { 3 } x ^ { 6 } + C$
C) $2 x + \frac { 5 } { 4 } x ^ { 4 } - \frac { 1 } { 4 } x ^ { 8 } + C$
D) $2 x + \frac { 5 } { 2 x ^ { 2 } } - \frac { 1 } { 3 x ^ { 6 } } + C$

Question

Quizplus · Accepted Answer

We can write the expression as:
$$\int \frac{2x^7}{x^7} \,dx - \int \frac{5x^4}{x^7} \,dx + \int \frac{2}{x^7} \,dx = 2x^{-6} - \frac{5}{-2}x^{-3} - \frac{1}{3}x^{-6} + C$$
Simplifying and adding the constants of integration, we get:
$$2x^{-6} + \frac{5}{2}x^{-3} - \frac{1}{3}x^{-6} + C = 2x + \frac{5}{2x^2} - \frac{1}{3x^6} + C$$
Therefore, the answer is D.

Find the Indefinite Integral ∫2x7−5x4+2x7dx\int \frac { 2 x ^ { 7 } - 5 x ^ { 4 } + 2 } { x ^ { 7 } } d x∫x72x7−5x4+2​dx

Find the Indefinite Integral $\int \frac { 2 x ^ { 7 } - 5 x ^ { 4 } + 2 } { x ^ { 7 } } d x$