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Find the integral $\int x^4\cos\left(5x\right)dx$

Used Formulas

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Solution

Formulas

Videos

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Trigonometric Integrals

· Integral of the cosine function
$\int\cos\left(\theta \right)dx=\sin\left(\theta \right)+C$
$\int\sin\left(ax\right)dx=-\left(\frac{1}{a}\right)\cos\left(ax\right)+C$
$\int\cos\left(ax\right)dx=\frac{1}{a}\sin\left(ax\right)+C$

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$

Function Plot

Plotting: $\frac{1}{5}x^4\sin\left(5x\right)+\frac{4}{25}x^{3}\cos\left(5x\right)-\frac{12}{125}x^{2}\sin\left(5x\right)-\frac{24}{625}x\cos\left(5x\right)+\frac{24}{3125}\sin\left(5x\right)+C_0$

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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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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.

Used Formulas

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