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

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

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integral of (xsqrt(x^2+3))

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = x^{2} + 3

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

Simplify

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

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

Add a constant to the solution

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

y^{^{''}} + 36 y = - 60 sec (6 t)

\int 12 (y^{4} + 4 y^{2} + 8)^{2} (y^{3} + 2 y) d y

\int x - 10 d x

\int sec^{5} (θ) d θ

C (x) = - 0.01 x^{2} + 7.2 x - 163

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