BASIC INTEGRATION PROBLEMS

I. Find the following integrals.

Problem 1 :

∫ (5x² - 8x + 5)dx

Solution:

Now we are going to write separate integration.

Problem 2 :

∫ (-6x³ + 9x² + 4x - 3)dx

Solution:

Problem 3 :

Solution:

Problem 4 :

Solution:

Problem 5 :

Solution:

Problem 6 :

Solution:

Problem 7 :

Solution:

Problem 8 :

Solution:

Problem 9 :

∫(1 + 3t)t² dt

Solution:

Problem 10 :

∫(2t² - 1)² dt

Solution:

Problem 11 :

Solution:

Problem 12 :

∫dθ

Solution:

= ∫dθ

= θ + C

Problem 13 : 

∫7 sin(x)dx

Solution:

= ∫7 sin(x)dx

= 7 ∫sin(x)dx

= 7(-cos(x))

= -7 cos x + C 

Problem 14 :

∫5 cos(θ) dθ

Solution:

= ∫5 cos(θ) dθ

= 5 ∫cos(θ) dθ

= 5 sin(θ) + C

Problem 15 :

∫9 sin(3x) dx

Solution:

= ∫9 sin(3x) dx

Let 3x = t

dx = 1/3 dt

= 9/3 ∫sin t dt

= 3 ∫sin t dt

= -3 cos t + C

= -3 cos(3x) + C