What is the integral from 1 to 2 of (x^5+3x^6)/(x^4) ?

The integral from 1 to 2 of (x^5+3x^6)/(x^4) is 17/2

Popular >

integral from 1 to 2 of (x^5+3x^6)/(x^4)

\int_{1}^{2} \frac{x ^{5} + 3 x ^{6}}{x ^{4}} d x

\frac{17}{2}

Decimal

8.5

Solution steps

\int_{1}^{2} \frac{x ^{5} + 3 x ^{6}}{x ^{4}} d x

Expand

\frac{x ^{5} + 3 x ^{6}}{x ^{4}} : \frac{x ^{5}}{x ^{4}} + \frac{3 x ^{6}}{x ^{4}}

Apply the Sum Rule:

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

= \int_{1}^{2} \frac{x ^{5}}{x ^{4}} d x + \int_{1}^{2} \frac{3 x ^{6}}{x ^{4}} d x

\int_{1}^{2} \frac{x ^{5}}{x ^{4}} d x = \frac{3}{2}

\int_{1}^{2} \frac{3 x ^{6}}{x ^{4}} d x = 7

= \frac{3}{2} + 7

Simplify

\frac{3}{2} + 7 : \frac{17}{2}

= \frac{17}{2}

\int_{2}^{B} (4 x - 3)^{3} d x

\int_{0}^{2} \frac{x}{1 + 4 x} d x

\int_{0}^{9} \frac{x}{x + 9} d x

\int_{0}^{x} t + 3 d t

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{8}} d x

What is the integral from 1 to 2 of (x^5+3x^6)/(x^4) ?
The integral from 1 to 2 of (x^5+3x^6)/(x^4) is 17/2