What is the integral of (5^{3x}+cosh(x)) ?

The integral of (5^{3x}+cosh(x)) is (125^x)/(3ln(5))+sinh(x)+C

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integral of (5^{3x}+cosh(x))

\int (5^{3 x} + cosh (x)) d x

\frac{12 5 ^{x}}{3 ln ( 5 )} + sinh (x) + C

Solution steps

\int 5^{3 x} + cosh (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5^{3 x} d x + \int cosh (x) d x

\int 5^{3 x} d x = \frac{12 5 ^{x}}{3 ln ( 5 )}

\int cosh (x) d x = sinh (x)

= \frac{12 5 ^{x}}{3 ln ( 5 )} + sinh (x)

Add a constant to the solution

= \frac{12 5 ^{x}}{3 ln ( 5 )} + sinh (x) + C

x \to 3 lim (2^{x})

\int tan^{5} (x) sec^{9} (x) d x

\int \frac{8 x ^{2} + 9 x + 8}{( x ^{2} + 1 ) ^{2}} d x

n = 0 \sum \infty (\frac{3}{7})^{n}

\frac{d y}{d x} = 9 x^{3}

What is the integral of (5^{3x}+cosh(x)) ?
The integral of (5^{3x}+cosh(x)) is (125^x)/(3ln(5))+sinh(x)+C