Find the indefinite integral:
\[
\int \frac{e^{7 x}}{e^{7 x}+36} d x
\]
$\frac{1}{7} e^{7 x}\left(e^{7 x}+36\right)+c$
$7 \ln \left(e^{7 x}+36\right)+c$
$\frac{1}{7} \ln \left(e^{7 x}+36\right)+c$
$7 e^{7 x} \ln \left(e^{7 x}+36\right)+C$

Answer

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Answer

Final Answer: The indefinite integral of the given function is $\boxed{\frac{1}{7} \ln \left(e^{7 x}+36\right)+c}$

Steps

Step 1 ：Find the indefinite integral: $\int \frac{e^{7 x}}{e^{7 x}+36} d x$

Step 2 ：The integral is a standard form of the integral of a function divided by its derivative plus a constant.

Step 3 ：This can be solved by using the formula for the integral of a function divided by its derivative plus a constant, which is the natural logarithm of the absolute value of the function plus a constant.

Step 4 ：Final Answer: The indefinite integral of the given function is $\boxed{\frac{1}{7} \ln \left(e^{7 x}+36\right)+c}$

Find the indefinite integral:\[\int \frac{e^{7 x}}{e^{7 x}+36} d x\]$\frac{1}{7} e^{7 x}\left(e^{7 x}+36\right)+c$$7 \ln \left(e^{7 x}+36\right)+c$$\frac{1}{7} \ln \left(e^{7 x}+36\right)+c$$7 e^{7 x} \ln \left(e^{7 x}+36\right)+C$

Answer

Popular Problems

Find the indefinite integral:
\[
\int \frac{e^{7 x}}{e^{7 x}+36} d x
\]
$\frac{1}{7} e^{7 x}\left(e^{7 x}+36\right)+c$
$7 \ln \left(e^{7 x}+36\right)+c$
$\frac{1}{7} \ln \left(e^{7 x}+36\right)+c$
$7 e^{7 x} \ln \left(e^{7 x}+36\right)+C$