What is the integral of sin^x(x ?

The integral of sin^x(x is (xsin^x(d))/(ln(sin(d)))-1/(ln^2(sin(d)))sin^x(d)+C

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integral of sin^x(x

\int sin^{x} (d) x d x

\frac{x sin ^{x} ( d )}{ln ( sin ( d ) )} - \frac{1}{ln ^{2} ( sin ( d ) )} sin^{x} (d) + C

Solution steps

\int sin^{x} (d) x d x

Apply Integration By Parts

: \frac{x sin ^{x} ( d )}{ln ( sin ( d ) )} - \int \frac{sin ^{x} ( d )}{ln ( sin ( d ) )} d x

= \frac{x sin ^{x} ( d )}{ln ( sin ( d ) )} - \int \frac{sin ^{x} ( d )}{ln ( sin ( d ) )} d x

\int \frac{sin ^{x} ( d )}{ln ( sin ( d ) )} d x = \frac{1}{ln ^{2} ( sin ( d ) )} sin^{x} (d)

= \frac{x sin ^{x} ( d )}{ln ( sin ( d ) )} - \frac{1}{ln ^{2} ( sin ( d ) )} sin^{x} (d)

Add a constant to the solution

= \frac{x sin ^{x} ( d )}{ln ( sin ( d ) )} - \frac{1}{ln ^{2} ( sin ( d ) )} sin^{x} (d) + C

\int \frac{t}{1 - t ^{2}} d t

sin (x) d x + y d y = 0, y (0) = - 2

\int \frac{1}{( x ^{2} + 10 x + 24 )} d x

\frac{d}{d x} (ln (arctan (x)))

\frac{d y}{d x} - 3 y = 0

What is the integral of sin^x(x ?
The integral of sin^x(x is (xsin^x(d))/(ln(sin(d)))-1/(ln^2(sin(d)))sin^x(d)+C