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indefinite integration

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

rebel

rebelmaths

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Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

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

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Students must find $\int \frac{1}{x-a} \, dx$.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

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

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

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  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Finding areas under graphs using definite integration.

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

Standard simple integrals asked for (1/x, sin(x), cos(x), x^2, x, e^x)

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4 questions on using partial fractions to solve indefinite integrals.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

A sneak peek at a really clever integration of GeoGebra with Numbas.

Integration by susbtitution, no hint given

Integration by susbtitution, no hint given

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.