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Find the integral $\int\left(1+4x^2e^{2x}+4\cdot e^3e^{2x}+x^4e^{2x}\right)dx$

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Solution

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Final answer to the problem

$x+2e^{\left(3+2x\right)}+\frac{7}{4}e^{2x}-\frac{7}{2}xe^{2x}+\frac{7}{2}x^2e^{2x}-e^{2x}x^{3}+\frac{1}{2}e^{2x}x^4+C_0$
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Learn how to solve tabular integration problems step by step online. Find the integral int(1+4x^2e^(2x)4e^3e^(2x)x^4e^(2x))dx. Simplify the expression. The integral \int1dx results in: x. Multiply the single term 4 by each term of the polynomial \left(\frac{1}{2}x^2e^{2x}-\frac{1}{2}xe^{2x}+\frac{1}{4}e^{2x}\right). Simplifying.

Final answer to the problem

$x+2e^{\left(3+2x\right)}+\frac{7}{4}e^{2x}-\frac{7}{2}xe^{2x}+\frac{7}{2}x^2e^{2x}-e^{2x}x^{3}+\frac{1}{2}e^{2x}x^4+C_0$

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Function Plot

Plotting: $x+2e^{\left(3+2x\right)}+\frac{7}{4}e^{2x}-\frac{7}{2}xe^{2x}+\frac{7}{2}x^2e^{2x}-e^{2x}x^{3}+\frac{1}{2}e^{2x}x^4+C_0$

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0
a
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n
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x
y
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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

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Main Topic: Tabular Integration

Tabular integration is a special technique to solve certain integrals by parts usually made up of two functions: one polynomial and the other transcendent, like the exponential function or the sine. The method consists of deriving the polynomial function several times (until it becomes zero), and integrating the transcendent function several times. This method is usually applied when both functions can be easily derived and integrated multiple times.

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