Questions: ∫(e^11u + 8u) du

Transcript text: \[ \int\left(e^{11 u}+8 u\right) d u \]

Solution

Solution Steps

Step 1: Split the Integral

We start with the integral \[ \int\left(e^{11 u}+8 u\right) d u. \] This can be separated into two integrals: \[ \int e^{11 u} du + \int 8u du. \]

Step 2: Evaluate Each Integral

For the first integral, we have: \[ \int e^{11 u} du = \frac{e^{11 u}}{11}. \]
For the second integral, we compute: \[ \int 8u du = 4u^2. \]

Step 3: Combine the Results

Combining the results from both integrals, we get: \[ \int\left(e^{11 u}+8 u\right) d u = \frac{e^{11 u}}{11} + 4u^2 + C, \] where \(C\) is the constant of integration.

Final Answer

Thus, the final result of the integral is \[ \boxed{\int\left(e^{11 u}+8 u\right) d u = \frac{e^{11 u}}{11} + 4u^2 + C}. \]

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