\( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x \) equals....
\( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x \) equals
\( \mathrm{P} \)
(1) \( -\frac{19}{36} x+\frac{35}{36} \log \left(9 e^{x}-4 e^{-x}\right)+c \)
(2) \( -\frac{3}{2} x+\frac{35}{36} \log \left(9 e^{2 x}-4\right)+c \)
(3) \( \frac{4}{9} x+\frac{70}{9} \int \frac{d x}{9 e^{2 x}-4}+c \)
(4) \( \frac{4}{9} x-\frac{70}{9} \int \frac{d x}{9 e^{2 x}-4}+c \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2024-01-22 | The area of bounded by the curve \( y=x^{2} \) and
\( y=\frac{2}{1+x^{2}} \), is.... |
| 2024-01-22 | The area bounded by the parabolas
\( x=-2 y^{2}, x=1-3 y^{2} \) is.... |
| 2024-01-22 | If \( \int \frac{\cot ^{3} x \cos x}{\left(\sin ^{5} x+\cos ^{5} x\right)^{3 / 5}} d x=\frac{-1}.... |
| 2024-01-22 | The area bounded by the curve \( x y^{2}=4(2-x) \) and
\( y \)-axis, is.... |
| 2024-01-22 | The area bounded by the curves \( y=\sin x \) and \( y= \)
\( \cos x \) between two consecutive .... |
| 2024-01-22 | The area bounded by the parabola \( y=x^{2}+1 \) and
the straight line \( x+y=3 \), is.... |
| 2024-01-22 | The area bounded by the curve \( y=(x-1)(x-2) \)
\( (x-3) \) lying between the ordinates \( x=1 .... |
| 2024-01-22 | Match the entries of Column-I with those of Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multic.... |
| 2024-01-22 | The area enclosed by the curves \( x^{2}=y, y=x+2 \),
and \( x \)-axis, is.... |
| 2024-01-22 | The area of bounded by \( x=2 y-y^{2} \) and the \( y \)-axis
is.... |
| 2024-01-22 | \( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x \) equals.... |
| 2024-01-22 | Match the items of Column-I with those in Column II.
\begin{tabular}{|l|l|l|l|}
\hline \multicol.... |
| 2024-01-22 | The area enclosed by the graph of \( y=\log _{\mathrm{e}}(x+1) \),
\( y \) - axis and the line \.... |
| 2024-01-22 | \( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This
rule is called subst.... |
| 2024-01-22 | \( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This
rule is called subst.... |
| 2024-01-22 | If \( \int \frac{x^{4}}{\sqrt{4+x^{5}}} d x=\frac{p}{q} \sqrt{4+x^{5}}+c \), then \( p+q=\ldots .... |
| 2024-01-22 | Let \( f(x)=x^{3}+a x^{2}+b x+c \) where \( a, b, c \) are real
numbers. If \( f(x) \) has local.... |
| 2024-01-22 | \( \int \frac{\sqrt{x}}{\sqrt{a^{3}-x^{3}}} d x= \).... |
| 2024-01-22 | \( \int \frac{x}{\left(x^{2}-3 x+2\right) \sqrt{x^{2}-4 x+3}} d x \) is equal to.... |
| 2024-01-22 | \( \int \frac{1-\cos x}{\cos x(1+\cos x)} d x \) is equal to.... |
| 2024-01-22 | \( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This
rule is called subst.... |
0