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Step-by-step Solution

Trigonometric integral int(x*cos(x))dx&pi/6&pi/2

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e
π
ln
log
lim
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sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch
Basic Derivatives
· Derivative of the linear function

The derivative of the linear function is equal to $1$

$\frac{d}{dx}\left(x\right)=1$
Trigonometric integrals

Apply the integral of the cosine function

$\int\cos\left(x\right)dx=\sin\left(x\right)+C$
Trigonometric identities
· Reciprocal identity of sine and cosecant

Applying the sine identity: $\displaystyle\sin\left(\theta\right)=\frac{1}{\csc\left(\theta\right)}$

$\sin\left(x\right)=\frac{1}{\csc\left(x\right)}$
$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.76 seconds

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