Integral of sin(1)^x

The calculator will find the integral/antiderivative of $$$\sin^{x}{\left(1 \right)}$$$, with steps shown.

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Find $$$\int \sin^{x}{\left(1 \right)}\, dx$$$.

The trigonometric functions expect the argument in radians. To enter the argument in degrees, multiply it by pi/180, e.g. write 45° as 45*pi/180, or use the appropriate function adding 'd', e.g. write sin(45°) as sind(45).

Solution

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=\sin{\left(1 \right)}$$$:

$${\color{red}{\int{\sin^{x}{\left(1 \right)} d x}}} = {\color{red}{\frac{\sin^{x}{\left(1 \right)}}{\ln{\left(\sin{\left(1 \right)} \right)}}}}$$

Therefore,

$$\int{\sin^{x}{\left(1 \right)} d x} = \frac{\sin^{x}{\left(1 \right)}}{\ln{\left(\sin{\left(1 \right)} \right)}}$$

Add the constant of integration:

$$\int{\sin^{x}{\left(1 \right)} d x} = \frac{\sin^{x}{\left(1 \right)}}{\ln{\left(\sin{\left(1 \right)} \right)}}+C$$

Answer

$$$\int \sin^{x}{\left(1 \right)}\, dx = \frac{\sin^{x}{\left(1 \right)}}{\ln\left(\sin{\left(1 \right)}\right)} + C$$$A

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Integral of $$$\sin^{x}{\left(1 \right)}$$$

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Solution

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