# University Maths Solution

Maths Question
Question 1

$\text{Evaluate }\int{{{x}^{10}}dx}$

Question 2

$\text{Evaluate }\int{3\sqrt{x}dx}$

Question 3

$\text{Evaluate }\int{\sqrt{{{x}^{3}}}}dx$

Question 4

$\text{Evaluate }\int{\frac{1}{\sqrt{4-{{x}^{2}}}}dx}$

Question 5

$\text{Evaluate }\int{\frac{1}{4+{{x}^{2}}}dx}$

Question 6

$\text{Evaluate }\int{\sec x\tan xdx}$

Question 7

$\text{Evaluate }\int{{{x}^{-1}}dx}$

Question 8

$\text{Evaluate }\int{{{(3u-5)}^{\tfrac{5}{2}}}}du$

Question 9

$\text{Evaluate }\int{\frac{dx}{{{x}^{2}}-2x+5}}$

Question 10

$\text{Evaluate }\int{\frac{dx}{\sqrt{15-4x-4{{x}^{2}}}}}$

Question 11

$\int{{{x}^{2}}dx}$

Question 12

$\text{Evaluate }\int\limits_{2}^{2\sqrt{3}}{\left( \frac{dx}{{{x}^{2}}+4} \right)}$

Question 13

$\text{Evaluate }\int\limits_{1}^{4}{\sqrt{(x+5)}dx}$

Question 14

$\text{Evaluate }\int\limits_{-3}^{3}{\frac{x}{{{x}^{2}}+5}dx}$

Question 15

$\text{Evaluate }\int\limits_{-1}^{1}{\frac{{{x}^{2}}+2x}{{{x}^{2}}+2x+2}dx}$

Question 16

$\text{Evaluate}\int{\frac{2x+3}{{{x}^{2}}+2x+10}dx}$

Question 17

$\text{Evaluate}\int{\sin x\cos xdx}$

Question 18

$\text{Evaluate }\int{{{\sin }^{3}}xdx}$

Question 19

$\text{Evaluate }\int\limits_{0}^{\tfrac{3}{2}}{\frac{dx}{{{x}^{2}}+9}}$

Question 20

$\text{Evaluate }\int{\frac{dx}{8+2x-{{x}^{2}}}}$

Question 21

$\text{Evaluate }\int{\frac{tdt}{1+4{{t}^{2}}}}$

Question 22

$\text{Evaluate }\int{\frac{x+1}{{{x}^{2}}+5x+6}dx}$

Question 23

$\int\limits_{{{e}^{4}}}^{{{e}^{2}}}{\frac{1}{x}\sin (\log x)dx}$

Question 24

$\int{{{\tan }^{5}}x{{\sec }^{2}}xdx}$

Question 25

$\text{Evaluate }\int{\sin 7x\sin 5xdx}$

Question 26

$\int{\frac{10dx}{(x-1)({{x}^{2}}+9)}}$

Question 27

$\text{Evaluate }\int{x{{e}^{-x}}dx}$

Question 28

$\int{{{x}^{3}}\sin x}dx$

Question 29

$\int{{{\theta }^{2}}\cos 2\theta d\theta }$

Question 30

$\text{Evaluate }\int{{{\sec }^{3}}xdx}$

Question 31

$\int{{{e}^{ax}}\cos bxdx}\text{ where }a\text{ and }b\text{ are constants using integration by part}\text{.}$

Question 23

$\text{Evaluate }\int{{{\sin }^{5}}x{{\cos }^{3}}xdx}$

Question 33

$\int_{0}^{1}{\frac{du}{\sqrt{3-2u}}}$

Question 34

$\int_{0}^{\sqrt{\tfrac{1}{3}}}{\frac{dx}{(2-3{{x}^{2}})}}$

Question 35

$\int{\frac{dx}{({{x}^{2}}+4)({{x}^{2}}+8)}}$

Question 36

$\int{\frac{5du}{(u+1)({{u}^{2}}+4)}}$

Question 37

$\text{Evaluate}\int{\frac{(6{{x}^{2}}+5x+2)dx}{{{(2x+1)}^{2}}(x-1)}}$

Question 38

$\text{Evaluate }\int_{0}^{2}{\frac{{{(\log x)}^{n}}}{x}dx}$

Question 39

$\int{\frac{1}{x}{{({{\log }_{e}}x)}^{3}}dx}$

Question 40

$\int{x\sqrt{{{a}^{2}}-{{x}^{2}}}}dx$