Use a table of integrals to find the indefinite integral $\int x ^ { 9 } e ^ { x ^ { 10 } } d x$ .
A) $\frac { 1 } { 9 } e ^ { x ^ { 10 } } + C$
B) $\frac { 1 } { 10 } e ^ { x ^ { 9 } } + C$
C) $\frac { 1 } { 10 } e ^ { x ^ { 10 } } + C$
D) $\frac { 1 } { 9 } e ^ { x ^ { 9 } } + C$
E) $\frac { 1 } { 10 } e ^ { x } + C$

Question

Quizplus · Accepted Answer

The integral $\int x^9 e^{x^{10}} dx$ can be solved by recognizing it as a form that results from the substitution method, where $u = x^{10}$ implies $du = 10x^9 dx$. Therefore, the integral becomes $\frac{1}{10} \int e^u du$, which evaluates to $\frac{1}{10} e^{x^{10}} + C$, making option C correct.

Use a Table of Integrals to Find the Indefinite Integral ∫x9ex10dx\int x ^ { 9 } e ^ { x ^ { 10 } } d x∫x9ex10dx

Use a Table of Integrals to Find the Indefinite Integral $\int x ^ { 9 } e ^ { x ^ { 10 } } d x$