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Mathematics practice questions
Integration
• Evaluate the following integrals.
1.



2. 
3. cos
3
x √sinx dx, (sinx>0).dx
4.



5.

󰇛

󰇜󰇛

󰇜

6.



7.

8.
󰇛
󰇜󰇛
󰇜

9.
    
10.


11.
∫ tan
2
x dx
12.



13.






14. ∫ 3ax/(b
2
+c
2
x
2
) dx
15. ∫tan
8
x sec
4
x dx
16.
∫ sin
3
x cos
2
x dx
17.
Write the anti-derivative of the following function: 3x
2
+4x
3
18.
1sinx1+cosxex2dx.
19. Show
that 2x+3x2+3xdx=logx2+3x+C∫2x+3x2+3xdx=llog|x^2+3x|
+C.
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20. 0π4(2sec2x+x3+2)dx

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Mathematics practice questions Integration • Evaluate the following integrals. 1. ∫ 3𝑥+1 𝑥2−𝑥−6 𝑑𝑥 2. ∫ 𝑐𝑜𝑠𝑒𝑐 𝑥 𝑑𝑥 3. ∫cos3x √sinx dx, (sinx>0).dx 4. ∫ 2𝑥 𝑑𝑥 𝑥6−1 5𝑥+8 5. ∫ 𝑑𝑥 (𝑥+3)(2𝑥−1) 9𝑥+6 6. ∫ 𝑥 3 −8 𝑑𝑥 9. ∫ 𝑥 𝑠𝑖𝑛𝑥 𝑑𝑥 ∫ (𝑥 + 1)(𝑥 − 3)𝑑𝑥 ∫ cos 3𝑥 sin 2𝑥 𝑑𝑥 10. ∫ 11. ∫ tan2x dx 12. ∫ 13. ∫ 7. 8. 1 1+𝑐𝑜𝑠𝑥 2𝑎 𝑑𝑥 𝑑𝑥 𝑥 2 −𝑎2 2𝑥 3 −9𝑥 2 +12𝑥 𝑑𝑥 2𝑥 2 −7𝑥+6 14. ∫ 3ax/(b2 +c2x2) dx 15. ∫tan8x sec4 x dx 16. ∫ sin3 x cos2x dx 17. Write the anti-derivative of the following function: 3x2+4x3 18. ∫ √1–sinx1+cosxe–x2dx. 19. Show that ∫2x+3x2+3xdx=log∣ +C. ∣ x2+3x∣ ∣ +C∫2x+3x2+3xdx=llog|x^2+3x| 20. ∫0π4(2sec2x+x3+2)dx Name: Description: ...
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