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Questions and Answers
In the integral $\int x^4 e^{3x} + 1 x^4 x e^{3x} dx$, what was the result of the integration?
In the integral $\int x^4 e^{3x} + 1 x^4 x e^{3x} dx$, what was the result of the integration?
- $ln x - 1$ (correct)
- $ln x - 4$
- $ln x$
- $ln x - 16$
When evaluating $\int (x^2 - 5x)e^x dx$, what is the final result after using the integration by parts method twice?
When evaluating $\int (x^2 - 5x)e^x dx$, what is the final result after using the integration by parts method twice?
- $(x^3 - 7x^2 + 7)e^x$
- $(x^3 - 5x^2 + 2x)e^x$
- $(x^2 - 5x + 2)e^x$
- $(x^2 - 7x + 7)e^x$ (correct)
What substitution was made for the integral $\int arcsin(x) dx$ before applying integration by parts?
What substitution was made for the integral $\int arcsin(x) dx$ before applying integration by parts?
- $u = cos(x)$
- $u = arcsin(x)$ (correct)
- $u = tan(x)$
- $u = sin(x)$
In the integral $\int x \sqrt{1 - x} dx$, what substitution was used to simplify the integral?
In the integral $\int x \sqrt{1 - x} dx$, what substitution was used to simplify the integral?
When evaluating $\int ln(x + x^2) dx$, what method was used to find the solution?
When evaluating $\int ln(x + x^2) dx$, what method was used to find the solution?
For the integral $\int sin(ln(x)) dx$, what substitution was applied before performing the integration?
For the integral $\int sin(ln(x)) dx$, what substitution was applied before performing the integration?
In $\int z(ln(z))^2 dz$, what is the correct substitution made before integrating by parts?
In $\int z(ln(z))^2 dz$, what is the correct substitution made before integrating by parts?
Considering $\int \sqrt{x} \cdot arcsin(x) dx$, what type of substitution would be most appropriate to simplify the integral?
Considering $\int \sqrt{x} \cdot arcsin(x) dx$, what type of substitution would be most appropriate to simplify the integral?
When evaluating $\int ln(arcsin(x)) dx$, what would be a valid initial substitution strategy?
When evaluating $\int ln(arcsin(x)) dx$, what would be a valid initial substitution strategy?
In the integral $\int sin(ln(x)) dx$, which subsequent method after substitution would be most effective for further simplification?
In the integral $\int sin(ln(x)) dx$, which subsequent method after substitution would be most effective for further simplification?
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