What is the integral of 6/(7x)+5e^{3x}+sqrt(x) ?

The integral of 6/(7x)+5e^{3x}+sqrt(x) is 6/7 ln|x|+5/3 e^{3x}+2/3 x^{3/2}+C

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integral of 6/(7x)+5e^{3x}+sqrt(x)

\int \frac{6}{7 x} + 5 e^{3 x} + x d x

\frac{6}{7} ln ∣ x ∣ + \frac{5}{3} e^{3 x} + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{6}{7 x} + 5 e^{3 x} + 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 \frac{6}{7 x} d x + \int 5 e^{3 x} d x + \int x d x

\int \frac{6}{7 x} d x = \frac{6}{7} ln ∣ x ∣

\int 5 e^{3 x} d x = \frac{5}{3} e^{3 x}

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

= \frac{6}{7} ln ∣ x ∣ + \frac{5}{3} e^{3 x} + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{6}{7} ln ∣ x ∣ + \frac{5}{3} e^{3 x} + \frac{2}{3} x^{\frac{3}{2}} + C

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What is the integral of 6/(7x)+5e^{3x}+sqrt(x) ?
The integral of 6/(7x)+5e^{3x}+sqrt(x) is 6/7 ln|x|+5/3 e^{3x}+2/3 x^{3/2}+C