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Find the integral $\int9t^3\cos\left(t^2\right)dt$

Used Formulas

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Solving: $\int9t^3\cos\left(t^2\right)dt$
Solve instead: $\int9t^3cos\left(t^2\right)dx$

Solution

Formulas

Videos

Basic Integrals

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

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
$\int udv=uv - \int vdu$

Trigonometric Integrals

· Integral of the cosine function
$\int\cos\left(\theta \right)dx=\sin\left(\theta \right)+C$
· Integral of the sine function
$\int\sin\left(\theta \right)dx=-\cos\left(\theta \right)+C$

Function Plot

Plotting: $\frac{9}{2}t^2\sin\left(t^2\right)+\frac{9}{2}\cos\left(t^2\right)+C_0$

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a
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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: Integration by Parts

Integration by parts is an integration method that relates the integral of a product of two or more functions to the integral of their derivative and antiderivative.

Used Formulas

See formulas (5)

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