What is the integral of 5xsqrt(x^2+9) ?

The integral of 5xsqrt(x^2+9) is 5/3 (x^2+9)^{3/2}+C

Popular >

integral of 5xsqrt(x^2+9)

\int 5 x x^{2} + 9 d x

\frac{5}{3} (x^{2} + 9)^{\frac{3}{2}} + C

Solution steps

\int 5 x x^{2} + 9 d x

Take the constant out:

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

= 5 \cdot \int x x^{2} + 9 d x

Apply u-substitution

: \int u^{2} d u

= 5 \cdot \int u^{2} d u

Apply the Power Rule

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

= 5 \cdot \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 9

= 5 \cdot \frac{( x ^{2} + 9 ) ^{3}}{3}

Simplify

5 \cdot \frac{( x ^{2} + 9 ) ^{3}}{3} : \frac{5}{3} (x^{2} + 9)^{\frac{3}{2}}

= \frac{5}{3} (x^{2} + 9)^{\frac{3}{2}}

Add a constant to the solution

= \frac{5}{3} (x^{2} + 9)^{\frac{3}{2}} + C

\int - x^{2} + 2 x + 3 d x

\int \frac{( x ^{3} + 4 x + 3 )}{x ^{4} + 5 x ^{2} + 4} d x

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

\int (x + 2) (x + 1) d x

\int \frac{x ^{3}}{( x + 3 ) ^{2}} d x

What is the integral of 5xsqrt(x^2+9) ?
The integral of 5xsqrt(x^2+9) is 5/3 (x^2+9)^{3/2}+C