1 of 8 0-day streak

Anti-differentiate a power of a linear function

Question 1 of 8

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G'(u)=2\,\left(u + 3\right)^{3}

\int 2\,\left(u + 3\right)^{3}\,du

Keep the original signed linear bracket unchanged in the primitive: do not expand, factor or rescale it. Enter exact values

(a)1 mark

Select the complete family of anti-derivatives

\int 2\,\left(u + 3\right)^{3}\,du

G(u)=\frac{1}{2}\,\left(u\right)^{4} + C

G(u)=\frac{1}{2}\,\left(u + 3\right)^{4} + C

G(u)=-\frac{1}{2}\,\left(u + 3\right)^{4} + C

G(u)=\frac{1}{2}\,\left(u + 3\right)^{3} + C

(b)4 marks

Enter the exact coefficient, original bracket parts and new exponent

G(u)=\square\,\left(\square\,u + \square\right)^{\square} + C

Outer coefficient Coefficient of the variable in the bracket Constant in the bracket New exponent