What is the integral of (7/x+(15)/(x^6)) ?

The integral of (7/x+(15)/(x^6)) is 7ln|x|-3/(x^5)+C

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integral of (7/x+(15)/(x^6))

\int (\frac{7}{x} + \frac{15}{x ^{6}}) d x

7 ln ∣ x ∣ - \frac{3}{x ^{5}} + C

Solution steps

\int \frac{7}{x} + \frac{15}{x ^{6}} 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{7}{x} d x + \int \frac{15}{x ^{6}} d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{15}{x ^{6}} d x = - \frac{3}{x ^{5}}

= 7 ln ∣ x ∣ - \frac{3}{x ^{5}}

Add a constant to the solution

= 7 ln ∣ x ∣ - \frac{3}{x ^{5}} + C

y = sin (2 x) cos (2 x)

\frac{\partial}{\partial x} ((\frac{x + 2}{y + 1})^{\frac{1}{2}})

e^{a s}

n \to \infty lim (- 3 + 4 n^{5})

\frac{\partial}{\partial y} (8 z e^{x yz})

What is the integral of (7/x+(15)/(x^6)) ?
The integral of (7/x+(15)/(x^6)) is 7ln|x|-3/(x^5)+C