Find the anti-derivative of the following function
\[ f(x) = 2x\]
\[ F(x) = x^2 + C \]
Find the anti-derivative of the following function \[ f(z) = 12 \]
\[F(z) = 12z\]
Find the anti-derivative of the following function
\[ f(x) = 12x^2 \]
\[F(x) = 4x^3 +C\]
Find the anti-derivative of the following function
\[ f(y) = sin(y) \]
\[ F(y) = -cos(y) + C \]
Find the anti-derivative of the following function
\[ f(\theta) = 2cos(\theta) \]
\[ F(\theta) = 2sin(\theta) + C \]
Find the anti-derivative of the following function
\[ g(x) = e^x \]
\[ G(x) = e^x + C\]
Find the anti-derivative of the following function
\[ h(z) = \frac{1}{z} \]
\[H(z) = ln(z) + C \]
Find the anti-derivative fo the following function
\[ f(x) = sec(x)tan(x) \]
\[ F(x) = sec(x) + C \]
Find the anti-derivative of the following function
\[ g(\theta) = \frac{4}{3}\theta\]
\[ G(\theta) = \frac{2}{3}\theta^{2} + C \]
Find the anti-derivative of the following function
\[ f(x) = -\frac{1}{x^3} \]
\[ F(x) = \frac{1}{2x^2} + C \]
Find the anti-derivative of the following function
\[ g(s) = \sqrt{s} \]
\[ G(s) = \frac{2}{3}\sqrt{s^3} + C \]
Find the anti-derivative of the following function
\[ h(x) = \frac{1}{\sqrt[3]{x^4}} \]
\[ -\frac{3}{\sqrt[3]{x}} + C \]
Find the anti-derivative of the following function
\[ f(q) = -csc^2(q) \]
\[ F(q) = cot(q) + C \]
Find the anti-derivative of the following function
\[ f(x) = 3x^2 + 2x + 1 \]
\[ F(x) = x^3 + x^2 + x + C \]
Find the anti-derivative of the following function
\[ g(x) = 2e^x - 5sin(x) \]
\[ G(x) = 2e^x + 5cos(x) + C\]
Find the anti-derivative of the following function
\[ h(y) = 0 \]
\[H(y) = C \]
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