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Find the integral $\int1\left(\frac{x^3e^{2x}}{-1}\right)dx$

Step-by-step Solution

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Solution

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Final Answer

$-\frac{1}{2}x^3e^{2x}+\frac{3}{4}x^{2}e^{2x}-\frac{3}{4}xe^{2x}+\frac{3}{8}e^{2x}+C_0$
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Step-by-step Solution

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Simplify the expression inside the integral

$\int-x^3e^{2x}dx$

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$\int-x^3e^{2x}dx$

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Learn how to solve simplification of algebraic expressions problems step by step online. Find the integral int((x^3e^(2x))/-11)dx. Simplify the expression inside the integral. The integral of a function times a constant (-1) is equal to the constant times the integral of the function. We can solve the integral \int x^3e^{2x}dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0.

Final Answer

$-\frac{1}{2}x^3e^{2x}+\frac{3}{4}x^{2}e^{2x}-\frac{3}{4}xe^{2x}+\frac{3}{8}e^{2x}+C_0$

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Solve integral of x^3e^2x/-11dx using partial fractionsSolve integral of x^3e^2x/-11dx using basic integralsSolve integral of x^3e^2x/-11dx using u-substitutionSolve integral of x^3e^2x/-11dx using integration by partsSolve integral of x^3e^2x/-11dx using tabular integrationSolve integral of x^3e^2x/-11dx using trigonometric substitution

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Function Plot

Plotting: $-\frac{1}{2}x^3e^{2x}+\frac{3}{4}x^{2}e^{2x}-\frac{3}{4}xe^{2x}+\frac{3}{8}e^{2x}+C_0$

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(◻)
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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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$\log\left(3\right)\cdot x+\log\left(27\right)\cdot x$

Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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