Find: (3 x-2) x 13 - ^2x - 7 x dx - Vidyadip

Question

$\text{Find}:\int\frac{(3\sin x-2)\cos x}{13\ -\ \cos^2x \ - \ 7\sin x}\text{d}x$

✓

Answer

$\int\frac{(3\sin\text{x}-2)\cos\text{x}}{13\ -\ \cos^2\text{x}\ -\ 7\sin\text{x}}\text{dx}$
$\int\frac{(3\sin\text{x}-2)\cos\text{x}}{\sin^2\text{x}\ -\ 7\sin\text{x}\ +12}\text{dx}$
put sin x = y, cos x dx = dy
$=\int\frac{(3\text{y}-2)\text{dy}}{\text{y}^2-7\text{y}+12}$
$=\int\frac{(3\text{y}-2)\text{dy}}{(\text{y}-4)(\text{y}-3)}$
$=\int\Big(\frac{10}{\text{y}-4}-\frac{7}{\text{y}-3}\Big)\text{dy}$
= 10 log | y – 4 | –7 log | y – 3 | + C
= 10 log | sin x – 4 | – 7 log | sin x – 3 | + C

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:

$\int\text{e}^{\text{x}}\frac{1+\text{x}}{(2+\text{x})^2}\text{dx}$

If f(x) = x² - 2x, find f(A), where $\text{A}=\begin{bmatrix}0&1&2\\4&5&0\\0&2&3\end{bmatrix}$

The two adjacent sides of a parallelogram are $2\hat i - 4\hat j + 5\hat k\;$ and $\hat i - 2\hat j - 3\hat k$. Find the unit vector parallel to its diagonal. Also, find its area.

Evaluate the following:
$\tan\frac{1}{2}\Big(\cos^{-1}\frac{\sqrt5}{3}\Big)$

Evaluate the following integrals:
$\int\sqrt{2\text{x}^2+3\text{x}+4}\text{dx}$

If $\vec{\alpha}=3\hat{\text{i}}+4\hat{\text{j}}+5\hat{\text{k}}$ and $\vec{\beta}=2\hat{\text{i}}+\hat{\text{j}}-4\hat{\text{k}},$ then express $\vec{\beta}$ in the form of $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2,$ where $\vec{\beta}_1$ is parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ is perpendicular to $\vec{\alpha}$.

Find the area of the region common to the parabolas 4y²= 9x and 3x²= 16y.

Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x²+ y² = 32.

Solve the following differential equation
$\text{x}\cos\text{y dy}=(\text{xe}^\text{x}\log\text{x}+\text{e}^\text{x})\text{dx}$

Find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes $\text{x + 2y +3z = 5 and 3x + 3y + z} = 0$