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

The integral of 2xsqrt(x^2+5) is 2/3 (x^2+5)^{3/2}+C

Popular >

integral of 2xsqrt(x^2+5)

\int 2 x x^{2} + 5 d x

\frac{2}{3} (x^{2} + 5)^{\frac{3}{2}} + C

Solution steps

\int 2 x x^{2} + 5 d x

Take the constant out:

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

= 2 \cdot \int x x^{2} + 5 d x

Apply u-substitution

: \int u^{2} d u

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

Apply the Power Rule

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

= 2 \cdot \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 5

= 2 \cdot \frac{( x ^{2} + 5 ) ^{3}}{3}

Simplify

2 \cdot \frac{( x ^{2} + 5 ) ^{3}}{3} : \frac{2}{3} (x^{2} + 5)^{\frac{3}{2}}

= \frac{2}{3} (x^{2} + 5)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x^{2} + 5)^{\frac{3}{2}} + C

\int \frac{3 x}{( 1 - 4 x ^{2} ) ^{2}} d x

x \to - 4 lim (2 x^{7} + 8 x^{4} - 1)

\int (y e^{y^{2}}) d y

x (x - 2)

\frac{d}{d t} (\frac{a + b t + c t ^{2}}{t})

What is the integral of 2xsqrt(x^2+5) ?
The integral of 2xsqrt(x^2+5) is 2/3 (x^2+5)^{3/2}+C