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