What is the integral of 7x(x^2+5)^4 ?

The integral of 7x(x^2+5)^4 is 7/10 (x^2+5)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7x(x^2+5)^4

\int 7 x (x^{2} + 5)^{4} d x

\frac{7}{10} (x^{2} + 5)^{5} + C

Solution steps

\int 7 x (x^{2} + 5)^{4} d x

Take the constant out:

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

= 7 \cdot \int x (x^{2} + 5)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{2} d u

= 7 \cdot \int \frac{u ^{4}}{2} d u

Take the constant out:

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

= 7 \cdot \frac{1}{2} \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 7 \cdot \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = x^{2} + 5

= 7 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{5}}{5}

Simplify

7 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{5}}{5} : \frac{7}{10} (x^{2} + 5)^{5}

= \frac{7}{10} (x^{2} + 5)^{5}

Add a constant to the solution

= \frac{7}{10} (x^{2} + 5)^{5} + C

\int e^{3 x} 1 + e^{3 x} d x

\int \frac{1}{4 u} d u

\int \frac{x - 1}{x ^{2}} e^{x} d x

\int sec^{2} (4 x) tan (4 x) d x

\int cos (\frac{nπ}{L} x) d x

What is the integral of 7x(x^2+5)^4 ?
The integral of 7x(x^2+5)^4 is 7/10 (x^2+5)^5+C