Try now NerdPal! Our new app on iOS and Android
Calculators Topics Solving Methods Step Checker
Book solutions
Algebra Baldor
Go Premium
ENG • ESP
Topics

Find the integral $\int\left(1+x+e^{\left(x-2\right)}\right)dx$

Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Solution

Formulas

Videos

Final Answer

$x+\frac{1}{2}x^2+e^{\left(x-2\right)}+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

$\int\left(1+x+e^{\left(x-2\right)}\right)dx$

Specify the solving method

1

Expand the integral $\int\left(1+x+e^{\left(x-2\right)}\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int1dx+\int xdx+\int e^{\left(x-2\right)}dx$

Learn how to solve integrals of exponential functions problems step by step online.

$\int1dx+\int xdx+\int e^{\left(x-2\right)}dx$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(1+xe^(x-2))dx. Expand the integral \int\left(1+x+e^{\left(x-2\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dx results in: x. The integral \int xdx results in: \frac{1}{2}x^2. The integral \int e^{\left(x-2\right)}dx results in: e^{\left(x-2\right)}.

Final Answer

$x+\frac{1}{2}x^2+e^{\left(x-2\right)}+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(1+xe^(x-2))dx using partial fractionsSolve int(1+xe^(x-2))dx using basic integralsSolve int(1+xe^(x-2))dx using u-substitutionSolve int(1+xe^(x-2))dx using integration by partsSolve int(1+xe^(x-2))dx using tabular integrationSolve int(1+xe^(x-2))dx using trigonometric substitution

Give us your feedback!

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

Compute the integral

$\int e^x\cos\left(x\right)dx$

Compute the integral

$\int xe^{2x}dx$

Compute the integral

$\int xe^{3x}dx$

Compute the integral

$\int3\cdot e^x\cdot xdx$

Compute the integral

$\int7\cdot e^{8x}\cdot xdx$

Compute the integral

$\int y^2 e^{2y}dy$

Compute the integral

$\int\sin\left(x\right)e^xdx$

Main topic:

Integrals of Exponential Functions

Used formulas:

5. See formulas

Time to solve it:

~ 0.05 s

Related topics:

Integrals of Exponential FunctionsIntegral CalculusCalculus

Supercharge your math learning

Use your academic email to get more benefits.
By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot password?

Supercharge your math learning

Use your academic email to get more benefits.


Register here if you don't have an account.
Forgot password?

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Including multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android app.

Join 500k+ students in problem solving.

Subscription. Cancel anytime.
Have a promo code?
Pay $2.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account
3-Month Special Plan
One-time payment of $2.97 USD.
Without automatic renewal.
Create an Account