What is the integral of 7xsqrt(x^2+3) ?

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

Popular >

integral of 7xsqrt(x^2+3)

\int 7 x x^{2} + 3 d x

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

Solution steps

\int 7 x x^{2} + 3 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} + 3 d x

Apply u-substitution

: \int u^{2} d u

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

Apply the Power Rule

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

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

Substitute back

u = x^{2} + 3

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

Simplify

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

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

Add a constant to the solution

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

\int 6 x^{2} a r cos (x) d x

\int \frac{1}{4 y - 1} d y

\int \frac{x - 1}{x ^{2} - 5 x + 6} d x

\int (1 + x^{7})^{5} 7 x^{6} d x

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

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