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