What is the integral from 1 to 2 of (x^4+3x^7)/(x^5) ?

The integral from 1 to 2 of (x^4+3x^7)/(x^5) is ln(2)+7

Popular >

integral from 1 to 2 of (x^4+3x^7)/(x^5)

\int_{1}^{2} \frac{x ^{4} + 3 x ^{7}}{x ^{5}} d x

ln (2) + 7

Solution steps

\int_{1}^{2} \frac{x ^{4} + 3 x ^{7}}{x ^{5}} d x

Simplify

\frac{x ^{4} + 3 x ^{7}}{x ^{5}} : \frac{1 + 3 x ^{3}}{x}

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

Expand

\frac{1 + 3 x ^{3}}{x} : \frac{1}{x} + 3 x^{2}

= \int_{1}^{2} \frac{1}{x} + 3 x^{2} 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_{1}^{2} \frac{1}{x} d x + \int_{1}^{2} 3 x^{2} d x

\int_{1}^{2} \frac{1}{x} d x = ln (2)

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

= ln (2) + 7

\int_{0}^{4} (4 x^{3} - 9 x^{2} + 2 x - 1) d x

\int_{- \frac{π}{3}}^{0} tan (x) d x

\int_{1}^{4} x - \frac{1}{x ^{2}} d x

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

\int_{- 1}^{1} (x^{5} - x^{6}) d x

What is the integral from 1 to 2 of (x^4+3x^7)/(x^5) ?
The integral from 1 to 2 of (x^4+3x^7)/(x^5) is ln(2)+7