Determine the integral by making an appropriate substitution.
-$\int ( x - 1 ) ^ { 7 } d x$
A) $\frac { 1 } { 2 }$ $x ^ { 2 }$ + $\frac { 1 } { 8 }$ $( x - 1 ) ^ { 8 }$ + C
B) $\frac { 1 } { 9 }$ $( x - 1 ) ^ { 9 }$ + $\frac { 1 } { 8 }$ $( x - 1 ) ^ { 8 }$ + C
C) $\frac { 1 } { 8 }$ $( x - 1 ) ^ { 8 }$ + C
D) $\frac { 1 } { 16 ( x - 1 ) ^ { 8 } }$ + C

Question

Determine the integral by making an appropriate substitution. 
-$\int ( x - 1 ) ^ { 7 } d x$
A) $\frac { 1 } { 2 }$ $x ^ { 2 }$ + $\frac { 1 } { 8 }$ $( x - 1 ) ^ { 8 }$ + C
B) $\frac { 1 } { 9 }$ $( x - 1 ) ^ { 9 }$ + $\frac { 1 } { 8 }$ $( x - 1 ) ^ { 8 }$ + C
C) $\frac { 1 } { 8 }$ $( x - 1 ) ^ { 8 }$ + C
D) $\frac { 1 } { 16 ( x - 1 ) ^ { 8 } }$ + C

Quizplus · Accepted Answer

The integral of $(x - 1)^7 dx$ is found by applying the power rule for integration, which gives $\frac{1}{8}(x - 1)^8 + C$.

Determine the Integral by Making an Appropriate Substitution ∫(x−1)7dx\int ( x - 1 ) ^ { 7 } d x∫(x−1)7dx

Determine the Integral by Making an Appropriate Substitution $\int ( x - 1 ) ^ { 7 } d x$