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Classes
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Aptitude Tests

Browse Worksheets
Classes
- Grade 9
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Aptitude Tests

ECAT Maths XII : Chapter 6 INTEGRATION (test 1)

Leave a Comment / By Afshan JAMAL / July 3, 2026

Welcome to your ECAT Maths XII : Chapter 6 INTEGRATION (test 1)

For n ≠ −1, ∫(ax + b)ⁿ dx =

(ax + b)ⁿ⁺¹/(n + 1) + C

(ax + b)ⁿ⁺¹/[a(n + 1)] + C

na(ax + b)ⁿ⁻¹ + C

a(ax + b)ⁿ⁻¹/[a(n + 1)] + C

None

Evaluate ∫(2x + 3)⁴ dx =

(2x + 3)⁵/5 + C

4(2x + 3)³ + C

(2x + 3)⁵/10 + C

8(2x + 3)³ + C

None

Evaluate ∫1/x³ dx =

−2√x + C

−2/√x + C

−1/(2x²) + C

1/(2x²) + C

None

Evaluate ∫3ᵃˣ dx =

(1/a)3ᵃˣ + C

(ln 3/a)3ᵃˣ + C

3ᵃˣ/ln 3 + C

3ᵃˣ/(a ln 3) + C

None

Evaluate ∫₋₂⁻¹ 1/(5 − 2x) dx =

ln(5/2)

ln(√(9/7))

−1/2 (ln 7 − ln 9)

Both B & C

None

Evaluate ∫(x + 7)/(x + 9) dx =

x − 2 ln(x + 9) + C

x − 2 ln(x) + C

x ln x + C

x − 2 ln(x + 7) + C

None

Evaluate ∫₀³ ∛(3t − 1)² dt =

31/5

37/5

33/5

7

None

Evaluate ∫eˡⁿ√x dx =

(2/3)x³ᐟ² + C

(3/2)x²ᐟ³ + C

−(2/3)x³ᐟ² + C

−(3/2)x²ᐟ³ + C

None

Evaluate ∫[(1/5)ˣ + (1/2)ˣ] dx = (a) (b) (c) (d)

5⁻ˣ/ln(5) + 2⁻ˣ/ln(2) + C

5⁻ˣ/ln(2) + 2⁻ˣ/ln(5) + C

5⁻ˣ/(−ln(5)) + 2⁻ˣ/(−ln(2)) + C

None of these

None

Evaluate ∫(e⁵ˣ + e³ˣ)/(eˣ + e⁻ˣ) dx =

e⁴ˣ/4 + C

−e⁴ˣ/4 + C

e⁴ˣ + C

−e⁴ˣ/3 + C

None

Evaluate ∫₋₃⁻¹ 1/(x − 1)³ dx =

4/31

4/3

−4/33

−31/32

None

Evaluate ∫x/(a + bx) dx =

x/b + (a/b) ln(a + bx) + C

x/b − (a/b²) ln(a + bx) + C

−x/b + (a/b) ln(ax + b) + C

−x/b + (a/b²) ln(ax + b) + C

None

∫ sinx dx =

cosx + c

-sinx + c

- cosx + c

sinx + c

None

Evaluate ∫₀¹ 1/(√(1 + x) − √x) dx =

4/3

√2/3

4√2/3

4√2

None

Evaluate ∫1/[x√(ln(9x))] dx =

2√(ln(9x)) + C

√(ln(81x²)) + C

Both A & B

2ln(9x) + C

None

Evaluate ∫sec x tan x dx =

cosec x + C

−cosec x + C

−sec x + C

sec x + C

None

Evaluate ∫cosec x cot x dx =

cosec x + C

−cosec x + C

−sec x + C

sec x + C

None

Find the primitive of (x² + 2)/(x² + 1) with respect to x.

(x² + 1)²/2 + x² + 1 + C

(x² + 1)² + (x² − 1)/2 + C

(x² + 1)²/2 + C

None of these

None

Evaluate ∫cos x dx =

sin x + C

−sin x + C

cos x + C

−cos x + C

None

Evaluate ∫sec²x dx =

1 + tan²x + C

tan x + C

−tan x + C

cot x + C

None

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