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

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

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 $kx e^{ax^2}$ using integration by substitution, where $k=2a$.

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 $\frac{nx+k}{(x+a)(x+b)(x+c)}$ 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.

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 $\frac{n}{(x+a)(x+b)^2}$ using partial fractions.

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.

Find the derivative of a function of the form $y=a \tan(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Calculating the derivative of an exponential function of the form $ae^{bx}$, using a table of derivatives.

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

Find the derivative of a function of the form $y=a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of derivatives.

Calculating the derivative of a function of the form $\frac{(x^2-a)^n}{x^2+a}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{ax^n+bx}{ax^n-bx}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{\ln(x)}{ax^n}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{e^{kx}}{ax^2+bx+c}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{a\sin(x)}{bx+c \cos(x)}$ using the quotient rule.