Topic

Indefinite Integrals with Complex Indices

Topic Progress:


\( \begin{aligned} \displaystyle \require{color} \int{\sqrt[n]{x^m}}dx &= \int{x^{\frac{m}{n}}}dx \\ &= \dfrac{x^{\frac{m}{n}+1}}{\frac{m}{n}+1} + C \\ \\ \int{\dfrac{1}{x^n}}dx &= \int{x^{-n}}dx \\ &= \dfrac{x^{-n+1}}{-n+1} + C \\ \end{aligned} \)

Practice Questions

Question 1

Find \( \displaystyle \int{x^{\frac{2}{3}}}dx \).

Question 2

Find \( \displaystyle \int{\sqrt{x}}dx \).

Question 3

Find \( \displaystyle \int{6x^2\sqrt{x}}dx \).

Question 4

Find \( \displaystyle \int{\sqrt[3]x}dx \).

Question 5

Find \( \displaystyle \int{\sqrt[4]{x^3}}dx \).

Question 6

Find \( \displaystyle \int{x\sqrt{x}}dx \).

Question 7

Find \( \displaystyle \int{\sqrt{9x}}dx \).

Question 8

Find \( \displaystyle \int{\sqrt[3]{8x^4}}dx \).

Question 9

Find \( \displaystyle \int{\sqrt[3]{2x^5}}dx \).

Question 10

Find \( \displaystyle \int{\dfrac{3}{\sqrt{x}}}dx \).

Question 11

Find \( \displaystyle \int{\dfrac{3x^2-x}{\sqrt{x}}}dx \).

Question 12

Find \( \displaystyle \int{\dfrac{1}{x^2}}dx \).

Question 13

Find \( \displaystyle \int{\dfrac{1}{2x^3}}dx \).

Question 14

Find \( \displaystyle \int{\dfrac{4}{3x^4}}dx \).

Question 15

Find \( \displaystyle \int{\sqrt[3]{x^5}}dx \).

Question 16

Find \( \displaystyle \int{\sqrt{5x^3}}dx \).

Question 17

Find \( \displaystyle \int{\frac{3x-1}{\sqrt{x}}}dx \).

Question 18

Find \( \displaystyle \int{(\sqrt{x}+1)^2}dx \).

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