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Integration by partial fractions
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Question in Bill's workspace by Bill Foster and 1 other

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.
Numbas demo: video
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Leicester: Integration 3
Draft
Question in Bill's workspace by Bill Foster

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.
Integration: Indefinite integral
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Indefinite integral: polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$ .
Indefinite integral by substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Indefinite integral by substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Integration by parts
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx$
Integration: Indefinite integral
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Integration: Indefinite integral
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Integration by partial fractions
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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.
Integration by partial fractions
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.
Integration by parts
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx$ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$
Julie's copy of Indefinite integral by substitution
Draft
Question in Julie's workspace by Julie Crowley

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Julie's copy of Indefinite integral
Draft
Question in Julie's workspace by Julie Crowley

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Julie's copy of Indefinite integral
Draft
Question in Julie's workspace by Julie Crowley

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Indefinite integral by substitution
Draft
Question in Julie's workspace by Julie Crowley

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.

rebelmaths
Question 2
Draft
Question in TEAME's workspace by TEAME UCC

indefinite integration

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

rebel

rebelmaths
YJ's copy of Numbas demo: video
Ready to use
Question in YJ's workspace by YJ Kim

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
Integration by parts 3 - exponential
Ready to use
Question in joshua's workspace by joshua boddy

Find $\displaystyle \int (ax)e^{cx}\; dx$
Integration by parts 2 - cos and sin with limits
Ready to use
Question in joshua's workspace by joshua boddy

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$
Integration by parts 4 - logarithm with limits
Ready to use
Question in joshua's workspace by joshua boddy

Find $\displaystyle \int (ax)\ln(cx)\; dx$
Integration by parts 3 - exponential with limits
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Question in joshua's workspace by joshua boddy

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

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