👉 Try now NerdPal! Our new math app on iOS and Android

Find the integral $\int\left(\left(e^x\right)^2-8x-7\left(2x-8\right)\right)dx$

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
Dx
|◻|
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

Final Answer

$\frac{1}{2}e^{2x}-11x^2+56x+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

We could not solve this problem by using the method: Integrate by trigonometric substitution

1

Simplify $\left(e^x\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $x$ and $n$ equals $2$

$\int\left(e^{2x}-8x-7\left(2x-8\right)\right)dx$

Learn how to solve problems step by step online.

$\int\left(e^{2x}-8x-7\left(2x-8\right)\right)dx$

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

Create a free account and unlock a glimpse of this solution.

Learn how to solve problems step by step online. Find the integral int(e^x^2-8x-7(2x-8))dx. Simplify \left(e^x\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals 2. Solve the product -7\left(2x-8\right). Simplify the expression inside the integral. We can solve the integral \int e^{2x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.

Final Answer

$\frac{1}{2}e^{2x}-11x^2+56x+C_0$

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 integral of (e^x^2+-8x)dx using partial fractionsSolve integral of (e^x^2+-8x)dx using basic integralsSolve integral of (e^x^2+-8x)dx using u-substitutionSolve integral of (e^x^2+-8x)dx using integration by partsSolve integral of (e^x^2+-8x)dx using tabular integration

Give us your feedback!

Function Plot

Plotting: $\frac{1}{2}e^{2x}-11x^2+56x+C_0$

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
Dx
|◻|
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:

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

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

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account