Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integrate $te^{\left(5t+\pi \right)}$ with respect to x

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
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

Answer

$\frac{1}{5}e^{\left(5t+\pi \right)}t-\frac{1}{25}e^{\left(5t+\pi \right)}+C_0$

Step-by-step explanation

Problem to solve:

$\int t e^{\left(5t+\pi \right)}dt$
1

Use the integration by parts theorem to calculate the integral $\int te^{\left(5t+\pi \right)}dt$, using the following formula

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

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=t}\\ \displaystyle{du=dt}\end{matrix}$

Unlock this step-by-step solution!

Answer

$\frac{1}{5}e^{\left(5t+\pi \right)}t-\frac{1}{25}e^{\left(5t+\pi \right)}+C_0$
$\int t e^{\left(5t+\pi \right)}dt$

Main topic:

Integration by substitution

Used formulas:

6. See formulas

Time to solve it:

~ 0.8 seconds

Struggling with math?

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