Step-by-step Solution

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

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

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 $du$

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

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

Main topic:

Integration by parts

~ 1.61 seconds

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!