indefinite integrals

Question

The integral ∫x² dx equals

RankGuru · Accepted Answer

1. **Identify Rule**: Apply the Power Rule for integration, which states $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ for $n 
eq -1$.
2. **Substitution**: Here $n = 2$.
3. **Calculation**:
   - $\int x^2 dx = \frac{x^{2+1}}{2+1} + C$
   - $= \frac{x^3}{3} + C$.
4. **Constant of Integration**: The constant $C$ is added because differentiation of any constant is zero, making it an indefinite integral.

Rank Guru

indefinite integrals

Select the correct option:

More indefinite integrals Practice Questions

Evaluate $\int e^x (\frac{1+x\ln x}{x}) dx$ (Assume $x > 0$ and base $e$ for $\ln$ ).

The integral ∫sin(x) dx equals

The integral ∫(1/x) dx equals

The integral ∫eˣ dx equals

indefinite integrals

Select the correct option:

More indefinite integrals Practice Questions

Evaluate ∫ex(1+xln⁡xx)dx\int e^x (\frac{1+x\ln x}{x}) dx∫ex(x1+xlnx​)dx (Assume x>0x > 0x>0 and base eee for ln⁡\lnln).

The integral ∫sin(x) dx equals

The integral ∫(1/x) dx equals

The integral ∫eˣ dx equals

Evaluate $\int e^x (\frac{1+x\ln x}{x}) dx$ (Assume $x > 0$ and base $e$ for $\ln$ ).