# Step-by-step Solution

## Integral of e^tcos(t)

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ln
log
lim
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sin
cos
tan
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csc

asin
acos
atan
acot
asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

$\frac{1}{2}\left(e^t\cos\left(t\right)+e^t\sin\left(t\right)\right)+C_0$

## Step-by-step explanation

Problem to solve:

$\int\left(e^t\cos\left(t\right)\right)dt$
1

Use the integration by parts theorem to calculate the integral $\int e^t\cos\left(t\right)dt$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=e^t}\\ \displaystyle{du=e^tdt}\end{matrix}$

$\frac{1}{2}\left(e^t\cos\left(t\right)+e^t\sin\left(t\right)\right)+C_0$
$\int\left(e^t\cos\left(t\right)\right)dt$