10 Questions
In the integral $\int x^4 e^{3x} + 1 x^4 x e^{3x} dx$, what was the result of the integration?
$ln x - 1$
When evaluating $\int (x^2 - 5x)e^x dx$, what is the final result after using the integration by parts method twice?
$(x^2 - 7x + 7)e^x$
What substitution was made for the integral $\int arcsin(x) dx$ before applying integration by parts?
$u = arcsin(x)$
In the integral $\int x \sqrt{1 - x} dx$, what substitution was used to simplify the integral?
$u = 1 - x$
When evaluating $\int ln(x + x^2) dx$, what method was used to find the solution?
Substitution and integration by parts
For the integral $\int sin(ln(x)) dx$, what substitution was applied before performing the integration?
$u = ln(x)$
In $\int z(ln(z))^2 dz$, what is the correct substitution made before integrating by parts?
$u = ln(z)$
Considering $\int \sqrt{x} \cdot arcsin(x) dx$, what type of substitution would be most appropriate to simplify the integral?
$u = \sqrt{x}$
When evaluating $\int ln(arcsin(x)) dx$, what would be a valid initial substitution strategy?
$u = arcsin(x)$
In the integral $\int sin(ln(x)) dx$, which subsequent method after substitution would be most effective for further simplification?
$u$-substitution
Explore a problem involving evaluating a function and proving its properties. Investigate whether the function is even, odd, or neither. Practice manipulating expressions and understanding function behavior.
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