Integrals of Powers, Roots, and Reciprocals

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For Grade 12 calculus students. Rewrite each expression into power form before integrating, and remember to include the constant of integration C.

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Answer key

Evaluate the indefinite integral: integral of x^4 dx
(1/5)x^5 + C
Evaluate the indefinite integral: integral of 1/(x^3) dx
-1/(2x^2) + C (or -(1/2)x^(-2) + C)
Evaluate the indefinite integral: integral of sqrt(x) dx
(2/3)x^(3/2) + C
Evaluate the indefinite integral: integral of 5 / x dx
5*ln|x| + C
Evaluate the indefinite integral: integral of 1 / sqrt(x) dx
2*sqrt(x) + C (or 2x^(1/2) + C)
Evaluate the indefinite integral: integral of (3x^2 - 2/x + x^(1/3)) dx
x^3 - 2*ln|x| + (3/4)x^(4/3) + C
Evaluate the indefinite integral: integral of sqrt(2x + 1) dx
(1/3)(2x + 1)^(3/2) + C