What is the integral of 9xsqrt(x^2+4) ?

The integral of 9xsqrt(x^2+4) is 3(x^2+4)^{3/2}+C

Popular >

integral of 9xsqrt(x^2+4)

\int 9 x x^{2} + 4 d x

3 (x^{2} + 4)^{\frac{3}{2}} + C

Solution steps

\int 9 x x^{2} + 4 d x

Take the constant out:

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

= 9 \cdot \int x x^{2} + 4 d x

Apply u-substitution

: \int u^{2} d u

= 9 \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= 9 \cdot \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 4

= 9 \cdot \frac{( x ^{2} + 4 ) ^{3}}{3}

Simplify

9 \cdot \frac{( x ^{2} + 4 ) ^{3}}{3} : 3 (x^{2} + 4)^{\frac{3}{2}}

= 3 (x^{2} + 4)^{\frac{3}{2}}

Add a constant to the solution

= 3 (x^{2} + 4)^{\frac{3}{2}} + C

\int 11 x^{3} d x

\int \frac{sin ( x )}{2 + 5 cos ( x )} d x

\int \frac{1}{2 v + v ^{2}} d v

\int \frac{8 x - x ^{\frac{5}{2}} - 2 x}{x ^{2}} d x

\int \frac{sec ^{2} ( x )}{tan ( x ) + 1} d x

What is the integral of 9xsqrt(x^2+4) ?
The integral of 9xsqrt(x^2+4) is 3(x^2+4)^{3/2}+C