Question

∫(5x^3 e^4x )dx evaluate in parts*

Answer 1

\[∫(5x^3 e^4x )dx\]

Answer 2

so its 5x^4?

Answer 3

example

Answer 4

it has to be in this format

Answer 5

i think the d and I stands for derivative and integral on top but not sure

Answer 6

Are you sure its not
\[\displaystyle\int5x^3 e^{4x}\ dx\]
instead of
\[\displaystyle\int5x^3 e^4x\ dx\]

Answer 7

\begin{eqnarray*}
\int 5x^3e^{4x}\ dx &=&
\left(5x^3\right)\left(\frac{1}{4}e^{4x}\right) - \int \left(15x^2\right)\left(\frac{1}{4}e^{4x}\right)\ dx \\ &=&
\left(5x^3\right)\left(\frac{1}{4}e^{4x}\right) - \left[\left(15x^2\right)\left(\frac{1}{16}e^{4x}\right) - \int \left(30x\right)\left(\frac{1}{16}e^{4x}\right)\ dx\right] \\&=&
\left(5x^3\right)\left(\frac{1}{4}e^{4x}\right) - \left[\left(15x^2\right)\left(\frac{1}{16}e^{4x}\right) - \left[\left(30x\right)\left(\frac{1}{64}e^{4x}\right) - \int \frac{30}{64}e^{4x}\ dx\right]\right]
\end{eqnarray*}

Answer 8

Understand?

Answer 9

the solution is:\[\int\limits(5x ^{3} e ^{4x})dx= 5 x^{3}(4e ^{4x})-15x ^{2}16e ^{4x}+30x(64e ^{4x})-30(128e ^{4x})+c\]

=\[\int\limits(5x ^{3} e ^{4x})dx= 20 x^{3}(e ^{4x})-240x ^{2}e ^{4x}+1920x(e ^{4x})-3840(e ^{4x})+c\]

Answer 10

He doesn't just want the solution...
And you can simplify it further than you did.
\[\frac{5}{128}e^{4x}(32x^3-24x^2+12x-3)\]

Answer 11

sure to simplify sounds better.
and regarding the solution in detail, he didn't mention that.
but one may either the conventional formual of the integarting by parts, i.e: \[\int\limits u dv=uv-\int\limits vdu\]
but it's easier to use the tabular method of soliving integration by parts, that I have uesd here.

Answer 12

wolfram answer