Antiderivatives: Level 2 Challenges Practice Problems Online

\[ \large \int \sin (x) \, dx - \int \sin (x ) \, dx = \ ? \]

Determine the indefinite integral of the following expression: \[ (\tan{x}) ( \tan{x}+ \sec{x} ).\]

Details and Assumptions:

Use \(C\) as the constant of the integration.

If \(f(x)=\displaystyle \int f(x)dx\),

then \(\displaystyle \int \left( f''(x)+(f'(x))^2+(f(x))^3 \right)dx=0\) will give \[\displaystyle \sum_{r=1}^3 \dfrac{(f(x))^r}{r}=?\]

If \( f\left( \frac{3x-4}{3x+4} \right) = x + 2 \), then what is the antiderivative of \(f(x) \)?

Clarification: Take \(C\) as an arbitrary constant.

\[\frac{8}{3}\ln(x-1) + \frac{2x}{3} + C\] \[e^{x+2} \ln(\frac{3x - 4}{3x + 4}) + C\] \[e^{\frac{3x + 4}{3x - 4}} - \frac{x^2}{2} + C\] None of these choices \[\frac{-8}{3}\ln(x-1) + \frac{2x}{3} + C\] \[e^{x-2} \ln(\frac{3x - 4}{3x + 4}) + C\] \[e^{\frac{3x - 4}{3x + 4}} - \frac{x^2}{2} + C\]

If an antiderivative of \(f\left( x \right) \) is \({ e }^{ x }\) and that of \(g\left( x \right) \) is \(\cos { x } \), then \(\displaystyle \int { f\left( x \right) \cos { x } \ dx } +\int { g\left( x \right) { e }^{ x } \ dx } \) is equal to

Concept Quizzes

Challenge Quizzes

Antiderivatives: Level 2 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Antiderivatives