MASH Bath: Question Bank

Calculating the integral of a function of the form $\frac{\cos(x) \sin(x)}{(\sin(x)+a)^2}$ using integration by substitution.

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Calculating the integral of a function of the form $2ax(ax^2+b)^n$ using integration by substitution. $n$ is a positive or negative fraction.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution. $n$ is a positive or negative fraction.

Identifying which graph shows the function $y=\frac{x-a}{x+b}$

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{c}{(kx+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{cx+d}{(x+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{cx+d}{(x+a)^2}$ using partial fractions.

Calculating the integral of a function of the form $\frac{n}{(x+a)(x+b)(x+c)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{n}{(x+a)(x+b)^2}$ using partial fractions.

Calculating the integral of a function of the form $\frac{nx+k}{(x+a)(x+b)(x+c)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{nx+k}{(x+a)(x+b)^2}$ using partial fractions.

Calculating the integral of a function of the form $\frac{mx^2+nx+k}{(x+a)(x+b)(x+c)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{mx^2+nx+k}{(x+a)(x+b)^2}$ using partial fractions.

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Calculating the integral of a function of the form $e^{ax} \cos(x)$ using integration by parts.

Calculating the integral of a function of the form $\ln(ax)$ using integration by parts.

Calculating the integral of a function of the form $ax^2 e^{bx}$ using integration by parts.

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $x^n \ln(ax)$ using integration by parts.

Calculating the integral of a function of the form $(a+bx)\cos(x)$ using integration by parts.

Calculating the integral of a function of the form $ax e^{bx}$ using integration by parts.

Calculating the integral of a function of the form $ax \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $ax \sin(bx)$ using integration by parts.

Calculating the area enclosed between a cosine function and a quadratic function by integration. The limits (points of intersection) are given in the question.