What is the integral of 2x(x^2+10)^{30} ?

The integral of 2x(x^2+10)^{30} is 1/31 (x^2+10)^{31}+C

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integral of 2x(x^2+10)^{30}

\int 2 x (x^{2} + 10)^{30} d x

\frac{1}{31} (x^{2} + 10)^{31} + C

Solution steps

\int 2 x (x^{2} + 10)^{30} 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} + 10)^{30} d x

Apply u-substitution

= 2 \cdot \int \frac{u ^{30}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{30} d u

Apply the Power Rule

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{31}}{31}

Substitute back

u = x^{2} + 10

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 10 ) ^{31}}{31}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 10 ) ^{31}}{31} : \frac{1}{31} (x^{2} + 10)^{31}

= \frac{1}{31} (x^{2} + 10)^{31}

Add a constant to the solution

= \frac{1}{31} (x^{2} + 10)^{31} + C

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What is the integral of 2x(x^2+10)^{30} ?
The integral of 2x(x^2+10)^{30} is 1/31 (x^2+10)^{31}+C