Solution: Indefinite Integrals #3

Evaluate:

[latex]\Large{\int(e^t + sin(t) - 1)dt}[/latex]

Step 1:

We can first apply the integration to each term as follows:

[latex]\large{\int(e^t + \sin(t) – 1)dt = \int(e^t)dt +\int(\sin(t))dt – \int(1)dt}[/latex]

Step 2:

Now, we can use our knowledge of common integrals to evaluate each integral individually, as shown:

[latex]\large{\int(e^t)dt = e^t}[/latex]

[latex]\large{\int(\sin(t))dt = -\cos(t)}[/latex]

[latex]\large{\int(1)dt = t }[/latex]

Step 3:

Now, combining everything, we have:

[latex]\large{\int(e^t + \sin(t) – 1)dt = e^t – \cos(t) – t + C}[/latex]

Solution Complete!

Step 1:

We can first apply the integration to each term as follows:

[latex]\large{\int(e^t + \sin(t) – 1)dt}[/latex]

[latex]\large{ = \int(e^t)dt +\int(\sin(t))dt – \int(1)dt}[/latex]