What is the integral of (x^7-3x)/(x^6) ?

The integral of (x^7-3x)/(x^6) is (x^2)/2+3/(4x^4)+C

Popular >

integral of (x^7-3x)/(x^6)

\int \frac{x ^{7} - 3 x}{x ^{6}} d x

\frac{x ^{2}}{2} + \frac{3}{4 x ^{4}} + C

Solution steps

\int \frac{x ^{7} - 3 x}{x ^{6}} d x

Expand

\frac{x ^{7} - 3 x}{x ^{6}} : x - \frac{3}{x ^{5}}

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

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

\int \frac{3}{x ^{5}} d x = - \frac{3}{4 x ^{4}}

= \frac{x ^{2}}{2} - (- \frac{3}{4 x ^{4}})

Simplify

= \frac{x ^{2}}{2} + \frac{3}{4 x ^{4}}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{3}{4 x ^{4}} + C

\int \frac{4 x}{2 x} + 6 d x

\int x (x^{2} - 7)^{\frac{7}{2}} d x

\int \frac{sin ( 2 x )}{sin ( x ) cos ^{2} ( x )} d x

\int \frac{cos ^{5} ( x )}{sin ( x )} d x

\int \frac{4 x}{x ^{2} + 4} d x

What is the integral of (x^7-3x)/(x^6) ?
The integral of (x^7-3x)/(x^6) is (x^2)/2+3/(4x^4)+C