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Step-by-step Solution

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

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y
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e
π
ln
log
lim
d/dx
Dx
>
<
>=
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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

Integration by parts of definite integral

https://www.youtube.com/watch?v=vS3bpx5ubBI

Properties of integrals to evaluate definite integrals

https://www.youtube.com/watch?v=9FLYqh697xI

Integration by Parts (part 6 of Indefinite Integration)

https://www.youtube.com/watch?v=ouYZiIh8Ctc

Double integral 1 | Double and triple integrals | Multivariable Calculus | Khan Academy

https://www.youtube.com/watch?v=85zGYB-34jQ

Triple integrals 3 | Double and triple integrals | Multivariable Calculus | Khan Academy

https://www.youtube.com/watch?v=ZN2PfqZ4ihM
$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.76 seconds

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