What is the integral of 10x^5-10x^2+7 ?

The integral of 10x^5-10x^2+7 is (5x^6)/3-(10x^3)/3+7x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 10x^5-10x^2+7

\int 10 x^{5} - 10 x^{2} + 7 d x

\frac{5 x ^{6}}{3} - \frac{10 x ^{3}}{3} + 7 x + C

Solution steps

\int 10 x^{5} - 10 x^{2} + 7 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 10 x^{5} d x - \int 10 x^{2} d x + \int 7 d x

\int 10 x^{5} d x = \frac{5 x ^{6}}{3}

\int 10 x^{2} d x = \frac{10 x ^{3}}{3}

\int 7 d x = 7 x

= \frac{5 x ^{6}}{3} - \frac{10 x ^{3}}{3} + 7 x

Add a constant to the solution

= \frac{5 x ^{6}}{3} - \frac{10 x ^{3}}{3} + 7 x + C

\frac{d y}{d x} = \frac{x}{25 y}

\int_{0}^{1} 1 + x^{3} d x

x \to 1 lim (e^{x} (x^{3} - 4))

(5) (0.5)

f (x) = 5 sec (x)

What is the integral of 10x^5-10x^2+7 ?
The integral of 10x^5-10x^2+7 is (5x^6)/3-(10x^3)/3+7x+C