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Popular >

integral of 3xsqrt(x^2+1)

Solution

\int 3 x x^{2} + 1 d x

Solution

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

Solution steps

\int 3 x x^{2} + 1 d x

Take the constant out:

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

= 3 \cdot \int x x^{2} + 1 d x

Apply u-substitution

: \int u^{2} d u

= 3 \cdot \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = x^{2} + 1

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

Simplify

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (1/x-5/(16x^2+1))

\int (\frac{1}{x} - \frac{5}{16 x ^{2} + 1}) d x

integral of x^3-x^2+1

\int x^{3} - x^{2} + 1 d x

integral of zsqrt(4z+1)

\int z 4 z + 1 d z

integral of (1-2x)^{10}

\int (1 - 2 x)^{10} d x

integral of (3x^2+2x)e^{3x}

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

Frequently Asked Questions (FAQ)

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