Methods of Integration

(cod: P-71-64-11) Determine the integrals below:

(1) \(\displaystyle \int x \cos{x} \, dx\)

(2) \(\displaystyle \int_0^{\frac{\pi}{2}}e^x \cos{x} \, dx\)

(3) \(\displaystyle \int_0^1 \arctan\, x \, dx\).

(1) \(x\, \sin\, {x} - \cos{x} + C.\)

(2) \(\dfrac{e^{\pi/2} - 1}{2}\)

(3) \(\frac{\pi}{4} - \frac{1}{2} \ln2 \)

(1) \(x\, \sin\, {x} + \cos{x} + C.\)

(2) \(\dfrac{e^{\pi/2} - 1}{2}\)

(3) \(\frac{\pi}{4} - \frac{1}{2} \ln2 \)

(1) \(x\, \sin\, {x} - \cos{x} + C.\)

(2) \(\dfrac{\pi - e^{\pi/2}}{2}\)

(3) \(\frac{\pi}{2} - \frac{1}{2} \ln3 \)

(1) \(x\, \sin\, {x} + \cos{x} + C.\)

(2) \(\dfrac{e^{\pi/2} - 1}{2}\)

(3) \(\frac{\pi}{2} - \frac{1}{2} \ln3 \)

(1) \(x\, \sin\, {x} + \cos{x} + C.\)

(2) \(\dfrac{\pi - e^{\pi/2}}{2}\)

(3) \(\frac{\pi}{2} - \frac{1}{2} \ln3 \)