Indefinite Integrals Practice Problems
Problem: Indefinite Integrals #1
Evaluate:
[latex]\Large{\int(2x^2+3x-1)dx}[/latex]
Step 1:
We can first apply the integration to each term as follows:
[latex]\large{\int(2x^2+3x-1)dx = \int(2x^2)dx + \int(3x)dx – \int(1)dx}[/latex]
Step 2:
Now, we can use the integral power rule to evaluate each integral individually, as shown:
[latex]\large{\int(2x^2)dx = \frac{2}{3}x^3}[/latex]
[latex]\large{\int(3x)dx = \frac{3}{2}x^2}[/latex]
[latex]\large{\int(1)dx = x}[/latex]
Step 3:
Now, combining everything, we have:
[latex]\large{\int(2x^2+3x-1)dx = \frac{2}{3}x^3 + \frac{3}{2}x^2 – x + C}[/latex]
Solution Complete!
Step 1:
We can first apply the integration to each term as follows:
[latex]\large{\int(2x^2+3x-1)dx}[/latex]
[latex]\small{ = \int(2x^2)dx + \int(3x)dx – \int(1)dx}[/latex]
Step 2:
Now, we can use the integral power rule to evaluate each integral individually, as shown:
[latex]\large{\int(2x^2)dx = \frac{2}{3}x^3}[/latex]
[latex]\large{\int(3x)dx = \frac{3}{2}x^2}[/latex]
[latex]\large{\int(1)dx = x}[/latex]
Step 3:
Now, combining everything, we have:
[latex]\large{\int(2x^2+3x-1)dx}[/latex]
[latex]\large{ = \frac{2}{3}x^3 + \frac{3}{2}x^2 – x + C}[/latex]
Solution Complete!
Problem: Indefinite Integrals #2
Evaluate:
[latex]\Large{\int(3x^4-x^3+2x^{\frac{1}{3}}-x^{-2})dx}[/latex]
[latex]\Large{\int(3x^4-x^3+2x^{\frac{1}{3}}-x^{-2})dx}[/latex]
Step 1:
We can first apply the integration to each term as follows:
[latex]\large{\int(3x^4-x^3+2x^{\frac{1}{3}}-x^{-2})dx}[/latex]
[latex]\small{ = \int(3x^4)dx\: – \:\int(x^3)dx + \int(2x^{\frac{1}{3}})dx\: -\: \int(x^{-2})dx}[/latex]
Step 2:
Now, we can use the integral power rule to evaluate each integral individually, as shown:
Problem: Indefinite Integrals #3
Evaluate:
[latex]\Large{\int(e^t + sin(t) - 1)dt}[/latex]
[latex]\Large{\int(e^t + sin(t) - 1)dt}[/latex]
Problem: Indefinite Integrals #4
Given:
[latex]\Large{h'(x) = 3x^4 - 2x^3 -15x^2+ 3x - 1}[/latex]
Find [latex]h(x)[/latex]
Problem: Indefinite Integrals #5
Given:
[latex]\Large{f'(z) = 5z^{-3} + 2z^2 +\frac{4}{z^3} - 5}[/latex]
Find [latex]f(z)[/latex]
[latex]\Large{f'(z) = 5z^{-3} + 2z^2 +\frac{4}{z^3} - 5}[/latex]
Find [latex]f(z)[/latex]
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