5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Questions which rely on knowledge of standard integrals.

Find an integral by choosing a suitable substitution.

Integrate the product of two functions by the method of integration by parts.

Integrate various functions by rewriting them as partial fractions.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on using substitution to find indefinite integrals.

4 questions on integrating by parts.

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5 questions on using substitution to find indefinite integrals.

4 questions on integrating by parts.

4 questions on using partial fractions to solve indefinite integrals.

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Step by step solving for integration by substitution

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given that $\displaystyle \int^i_j x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

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 $