Indefinite Integration Practice Questions

JEE · Mathematics · 1858 free MCQs with instant results and detailed explanations.

1858

Total

384

Easy

856

Medium

618

Hard

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Topics in Indefinite Integration

Special Integrals 303

Trigonometric Integrals 390

Basic Formulas 270

By Parts 323

Substitution 248

Partial Fractions 324

Sample Questions from Indefinite Integration

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

What is the integral of e^x?

A. e^x + C

B. x + C

C. e^(x+1) + C

D. xe^x + C

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Correct Answer: A

The integral of e^x is itself, e^x, plus a constant of integration C.

Easy

Which of the following is the integral of x^2?

A. x^3/3 + C

B. 2x + C

C. x^2 + C

D. x^3 + C

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Correct Answer: A

The integral of x^2 is (x^3)/3 plus a constant of integration C, based on the power rule.

Easy

What is the integral of 1/x?

A. ln|x| + C

B. x + C

C. 1/x + C

D. ln(x) + C

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Correct Answer: A

The integral of 1/x is the natural logarithm of the absolute value of x, plus a constant of integration C.

Medium

Determine the integral of sec^2(x) dx.

A. tan(x) + C

B. sec(x) + C

C. sin(x) + C

D. cos(x) + C

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Correct Answer: A

The integral of sec^2(x) is known to be tan(x) plus a constant of integration C.

Medium

Find ∫ (1/(x^2 + 1)) dx.

A. tan^(-1)(x) + C

B. sin(x) + C

C. ln(x) + C

D. cos^(-1)(x) + C

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Correct Answer: A

The integral of 1/(x^2 + 1) is arctan(x) or tan^(-1)(x) plus C.

Medium

Evaluate the integral ∫ (sin(x)cos(x)) dx using a substitution.

A. -0.5 cos^2(x) + C

B. 0.5 sin^2(x) + C

C. -0.5 sin^2(x) + C

D. 0.5 cos^2(x) + C

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Correct Answer: A

Using the substitution u = sin(x), the integral simplifies to -0.5 cos^2(x) + C.

Medium

Determine ∫ (tan(x)) dx.

A. -ln(cos(x)) + C

B. ln(sin(x)) + C

C. sin(x) + C

D. cos(x) + C

Show Answer & Explanation

Correct Answer: A

The integral of tan(x) is -ln(cos(x)) + C, derived from the identities of tan and sec.

Hard

Evaluate the integral ∫ (2x^3 - 3x^2 + 1) dx.

A. (1/2)x^4 - x^3 + x + C

B. (1/2)x^4 - (3/3)x^2 + C

C. (1/4)x^4 - (1/3)x^3 + x + C

D. (1/4)x^4 - x^3 + C

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Correct Answer: A

The integral of a polynomial is obtained by increasing the degree by 1 and dividing by the new degree.

Hard

Calculate ∫ (ln(x))^2 dx.

A. x(ln(x))^2 - 2xln(x) + 2x + C

B. x(ln(x))^2 + 2xln(x) + C

C. x(ln(x))^2 + 2xln(x) - 2x + C

D. x(ln(x))^2 - xln(x) + C

Show Answer & Explanation

Correct Answer: A

This integral requires integration by parts performed twice.

Q10

Hard

Determine the integral ∫ (1/x) * e^(ln(x)) dx.

A. e^(ln(x)) + C

B. x + C

C. xln(x) + C

D. e^(ln(x) + C)

Show Answer & Explanation

Correct Answer: B

e^(ln(x)) simplifies to x, turning the integral into ∫ 1 dx.

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Indefinite Integration — JEE Mathematics Practice Questions Online

This page contains 1858 practice MCQs for the chapter Indefinite Integration in JEE Mathematics. The questions are organized by difficulty — 384 easy, 856 medium, 618 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 6 topics, giving you comprehensive coverage of the entire chapter.