\begin{align}
\int a^x + dx &= a^x \cdot \ln a + C\\
\int e^x \ dx &= e^x + C\\
\int e^{k\cdot x}&=\frac{1}{k}+e^{k\cdot x}+C\\
\int \frac{1}{x} \ dx &= \ln x + C
\end{align}

Oppgave 1

  • \begin{align}\int 2^{x} \ dx &=
    2^x\cdot \ln 2+C\end{align}

  • \begin{align}
    \int 2^{2x} \ dx &= \frac{1}{ 2}2^{2x}\cdot \ln 2 + C\end{align}

  • \begin{align}\int 3\cdot 3^{6x}
    &=\frac{3}{6}3^{6x}+C
    \end{align}

Oppgave 2

  • \begin{align}\int e^{2x} \ dx &=\frac{1}{2}e^{2x}+C\end{align}

  • \begin{align}
    \int 4 e^{2x} \ dx &= \frac{4}{2}e^{2x}\end{align}

Oppgave 3

  • \begin{align}\int \frac{1}{x} \ dx &=\ln x+C\end{align}

  • \begin{align}\int \frac{1}{2x} \ dx
    &=\int \frac{1}{2}\cdot \frac{1}{x} \ dx\\
    &=\frac{1}{2}\int \frac\{1}{x} \ dx\\
    &=\frac{1}{2}\ln x+C\end{align}