What is the integral of 7xsqrt(x^2+1) ?

The integral of 7xsqrt(x^2+1) is 7/3 (x^2+1)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 7xsqrt(x^2+1)

\int 7 x x^{2} + 1 d x

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

Solution steps

\int 7 x x^{2} + 1 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} + 1 d x

Apply u-substitution

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

Apply the Power Rule

= 7 \cdot \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 1

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

Simplify

7 \cdot \frac{( x ^{2} + 1 ) ^{3}}{3} : \frac{7}{3} (x^{2} + 1)^{\frac{3}{2}}

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

Add a constant to the solution

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

What is the integral of 7xsqrt(x^2+1) ?
The integral of 7xsqrt(x^2+1) is 7/3 (x^2+1)^{3/2}+C