The value of the integral int frac{sin(ln(2 + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $I = \int \frac{\sin(\ln(2 + 2x))}{x + 1} dx$. We can rewrite the argument of the logarithm as $2 + 2x = 2(1 + x)$. So,$I = \int \frac{\sin(\l

Vedclass · Accepted Answer

$- \cos(\ln(2x + 2)) + C$

Vedclass · Answer

(A) Let $I = \int \frac{\sin(\ln(2 + 2x))}{x + 1} dx$. We can rewrite the argument of the logarithm as $2 + 2x = 2(1 + x)$. So,$I = \int \frac{\sin(\ln(2(1 + x)))}{x + 1} dx = \int \frac{\sin(\ln 2 + \ln(1 + x))}{x + 1} dx$. Let $u = \ln(2 + 2x)$. Then $du = \frac{1}{2 + 2x} \cdot 2 dx = \frac{1}{1 + x} dx$. Substituting these into the integral,we get $I = \int \sin(u) du$. The integral of $\sin(u)$ is $-\cos(u) + C$. Substituting back $u = \ln(2 + 2x)$,we get $I = -\cos(\ln(2 + 2x)) + C$.

The value of the integral $\int \frac{\sin(\ln(2 + 2x))}{x + 1} dx$ is

Similar Questions

The integral $\int \frac{e^{3 \log_{e} 2x} + 5e^{2 \log_{e} 2x}}{e^{4 \log_{e} x} + 5e^{3 \log_{e} x} - 7e^{2 \log_{e} x}} dx$,where $x > 0$,is equal to ....... (where $c$ is a constant of integration).

$\int \frac{\sqrt{x-2}}{2x+4} dx=$

The integral $\int \frac{1}{\sqrt[4]{(x-1)^{3}(x+2)^{5}}} dx$ is equal to : (where $C$ is a constant of integration)

Integrate the function: $\frac{x^{2}}{1-x^{6}}$

$\int {\frac{{{e^{2x}} + 1}}{{{e^{2x}} - 1}}} \,dx$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module