Integrate 3^x: animated lesson

1. 1. The problem
   Evaluating an integral

   $\int {3}^{x}\,dx$
2. 2. Step by step
   1. $$\int {3}^{x}\,dx$$
      Start with the integral
   2. $$\int {3}^{x}\,dx = \frac{{3}^{x}}{\ln\left(3\right)}$$
      Exponential rule: ∫ aᵘ du = aᵘ/ln a
   3. $$\int {3}^{x}\,dx = \frac{{3}^{x}}{\ln\left(3\right)} + C$$
      Simplify and add the constant of integration
3. 3. The answer
   $$\frac{{3}^{x}}{\ln\left(3\right)} + C$$

   ∫ 3^x dx = 3^x / ln(3) + C

4. 4. Check
   • ✓Differentiated the answer and compared it with the integrand at 8 sample points ✓

Find antiderivatives with standard rules, substitution and integration by parts.

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