Questions: Find ∫(5x^6+2x^4) dx

Transcript text: Find $\int\left(5 x^{6}+2 x^{4}\right) d x$

Solution

Solution Steps

Step 1: Define the Integral

We start with the integral to solve: \[ \int \left(5 x^{6} + 2 x^{4}\right) \, dx \]

Step 2: Apply the Power Rule

Using the power rule for integration, we integrate each term separately:

For $5 x^{6}$: \[ \int 5 x^{6} \, dx = \frac{5}{7} x^{7} \]
For $2 x^{4}$: \[ \int 2 x^{4} \, dx = \frac{2}{5} x^{5} \]

Step 3: Combine the Results

Combining the results from the integration of both terms, we have: \[ \int \left(5 x^{6} + 2 x^{4}\right) \, dx = \frac{5}{7} x^{7} + \frac{2}{5} x^{5} + C \]

Final Answer

Thus, the complete solution to the integral is: \[ \boxed{\frac{5}{7} x^{7} + \frac{2}{5} x^{5} + C} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >