Find the indefinite integral. (Remember the constant of integration.)
$\int 4^{\sin (x)} \cos (x) d x$

Answer

Expert–verified

Hide Steps

Answer

$Final Answer: The indefinite integral of 4^{\sin (x)} \cos (x) with respect to x is \frac{4^{\sin (x)}}{2 \ln (2)} + C, where C is the constant of integration.$

Steps

Step 1 ：Let $u = \sin (x)$ , then $d u = \cos (x) d x$

Step 2 ：Substitute $u$ into the integral, the integral becomes $\int 4^{u} d u$

Step 3 ：Solve the integral directly to get $\frac{4^{u}}{\ln (4)}$

Step 4 ：Substitute $\sin (x)$ back for $u$ to get $\frac{4^{\sin (x)}}{\ln (4)}$

Step 5 ：Simplify the final answer to get $\frac{4^{\sin (x)}}{2 \ln (2)}$

Step 6 ： $Final Answer: The indefinite integral of 4^{\sin (x)} \cos (x) with respect to x is \frac{4^{\sin (x)}}{2 \ln (2)} + C, where C is the constant of integration.$

Find the indefinite integral. (Remember the constant of integration.)∫4sin⁡(x)cos⁡(x)dx

Answer

Popular Problems

Find the indefinite integral. (Remember the constant of integration.)
$\int 4^{\sin (x)} \cos (x) d x$