What is the integral of (3x^5-7x^3)/(x^2) ?

The integral of (3x^5-7x^3)/(x^2) is 1/12 (3x^2-7)^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x^5-7x^3)/(x^2)

\int \frac{3 x ^{5} - 7 x ^{3}}{x ^{2}} d x

\frac{1}{12} (3 x^{2} - 7)^{2} + C

Solution steps

\int \frac{3 x ^{5} - 7 x ^{3}}{x ^{2}} d x

Simplify

\frac{3 x ^{5} - 7 x ^{3}}{x ^{2}} : x (3 x^{2} - 7)

= \int x (3 x^{2} - 7) d x

Apply u-substitution

: \int \frac{u}{6} d u

= \int \frac{u}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{1}{6} \cdot \frac{u ^{2}}{2}

Substitute back

u = 3 x^{2} - 7

= \frac{1}{6} \cdot \frac{( 3 x ^{2} - 7 ) ^{2}}{2}

Simplify

\frac{1}{6} \cdot \frac{( 3 x ^{2} - 7 ) ^{2}}{2} : \frac{1}{12} (3 x^{2} - 7)^{2}

= \frac{1}{12} (3 x^{2} - 7)^{2}

Add a constant to the solution

= \frac{1}{12} (3 x^{2} - 7)^{2} + C

\int (x + 1) cos (x^{2} + 2 x + 1) d x

\frac{d}{d x} (6 x^{2} - 18 x + 12)

x^{2}, - 4, 0

\int x^{5} x^{3} + 4 d x

\int_{0}^{\frac{π}{21}} tan (7 x) d x

What is the integral of (3x^5-7x^3)/(x^2) ?
The integral of (3x^5-7x^3)/(x^2) is 1/12 (3x^2-7)^2+C