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Popular >

integral of sin(1-x)(2-cos(1-x))^4

Solution

\int sin (1 - x) (2 - cos (1 - x))^{4} d x

Solution

- \frac{( 2 - cos ( 1 - x ) ) ^{5}}{5} + C

Solution steps

\int sin (1 - x) (2 - cos (1 - x))^{4} d x

Apply u-substitution

: \int - u^{4} d u

= \int - u^{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= - \frac{u ^{5}}{5}

Substitute back

u = 2 - cos (1 - x)

= - \frac{( 2 - cos ( 1 - x ) ) ^{5}}{5}

Add a constant to the solution

= - \frac{( 2 - cos ( 1 - x ) ) ^{5}}{5} + C

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\int (e^{3 p - 7}) d p

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\int \frac{3}{x ^{2} - 8 x + 13} d x

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\int \frac{2}{x ( x + 5 )} d x

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\int \frac{7}{2 + 3 y} d y

integral of 2cot^2(x)csc^4(x)

\int 2 cot^{2} (x) csc^{4} (x) d x

Frequently Asked Questions (FAQ)

What is the integral of sin(1-x)(2-cos(1-x))^4 ?
The integral of sin(1-x)(2-cos(1-x))^4 is -((2-cos(1-x))^5)/5+C