Use defintions of the hyperbolic functions to integrate by considering exponentials.

Rearrange and make a substitution to integrate a quotient to a function in terms of arsinh.

Rearrange and make a substitution to integrate a quotient to a function in terms of arsinh.

Use double angle an pythagorean identities to manipulate before integrating.

Integrating a function of the form $\frac{a}{x}$ using a table of integrals / anti-derivatives.

Integrating a polynomial functions which describe the rate of change of a population over time to find and use an equation that describes the total population according to time.

Integrating an exponential function of the form $ae^{bx}$ using a table of integrals / anti-derivatives.

Using the IF to find the General Solution.

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Also two other questions on integrating by parts.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Integrating by parts.

Find $ \int ax\sin(bx+c)\;dx$ or $\int ax e^{bx+c}\;dx$ 

4 questions on integrating by parts.

4 questions on integrating by parts.

4 questions on integrating by parts.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

4 questions on integrating by parts.

4 questions on integrating by parts.

4 questions on integrating by parts.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

4 questions on integrating by parts.

4 questions on integrating by parts.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $