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Find the integral $\int2x\left(7+\left(e^x\right)^2\right)dx$

Used Formulas

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Solution

Formulas

Videos

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$
· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Integral of a Constant
$\int cdx=cvar+C$
$\int e^xdx=e^x+C$
· Power Rule of Integration
$\int xdx=\frac{1}{2}x^2+C$

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$
· Integration by Parts
$\int udv=uv - \int vdu$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Function Plot

Plotting: $\left(14x+e^{2x}\right)x-7x^2-\frac{1}{2}e^{2x}+C_0$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
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(◻)
+
-
×
◻/◻
/
÷
◻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

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

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

Compute the integral

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

Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

Used Formulas

8. See formulas

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